CURRICULUM VITAE
1. Personal data:
a) First name: ALEXANDER
b) Family name: MESKHI
c) Date of birth: May 2, 1972.
d) Place of birth: Tbilisi, Georgia.
e) Citizenship: Citizen of Georgia.
f) Marital status: Married.
g) Children: Two sons
h) Codice Fiscale
(in Italy):
MSK LND 72E02 Z136S
i) Personal homepage: http://www.rmi.ge/~meskhi/
2. Positions:
a)11.05.2000up to now: Senior Researcher at A.Razmadze Mathematical Institute, Georgia.
b) 28.09.2009up to now: Full
Professor of the
Technical University of Georgia (Department of Mathematics).
b) 01.2006up to now: Foreign Professor of Abdus Salam School of Mathematical Sciences, GC University,
Lahore, Pakistan.
c) 01.05.2003 01.05.2005 : Postdoc
position at Scuola Normale Superiore of Pisa,
Italy.
d) 02.10.1998 11.05.2000: Researcher at A. Razmadze Mathematical Institute, Georgia.
3. Mailing Addresses:
A. Razmadze
Mathematical Institute of I. Javakhishvili Tbilisi
State University, 6 Tamarashvili Str., Tbilisi 0177,
Georgia.
4. email: meskhi@rmi.ge; alex72meskhi@yahoo.com
5. Tel. : (+995 32) 32 62 47;
(+995) 93 57 38 95.
6. Languages: Georgian (Mother), Russian, English, Italian.
7.
Education:
a) 19951998  Postgraduate Student of A. Razmadze Mathematical Institute
b) 19901995  Student of
the Technical
University of Georgia.
8. Scientific degrees:
a) 2001: Doctor of Sciences of Phys.Math.:
"Boundedness and compactness criteria for potential type operators". A. Razmadze Mathematical Institute (Scientific Consultant Prof. V.
Kokilashvili).
b) 1998 : Candidate Degree of Phys. Math
(Ph.D.) " Twoweight inequalities for singular integrals defined on
homogeneous groups". A. Razmadze Mathematical Institute (Supervisor Prof. V. Kokilashvili).
c) 1995: Master Degree in Mathematics, "
Twoweight inequalities for singular integrals and potentials on Heisenberg
groups". Technical
University of Georgia (Supervisor Prof. V. Kokilashvili).
9. Main Research Field: Harmonic Analysis and Applications in Partial
Differential Equations.
10. Main Topics: Weight theory of integral and differential
operators and applications in nonlinear partial differential equations;
spectral theory of integral operators; analysis on measure metric spaces;
function spaces; abstract harmonic analysis.
11. Research Grants:
a)
18.09.201124.09.2013: Shota Rustaveli National Science
Foundation Grant, Name of the Project: ‘’8the International Conference on
Function Spaces, Differential Operators, and Nonlinear Analysis’’, Project No. 11_tr_129.
b)
01.01.201001.01.2013: Shota Rustaveli National Science Foundation Grant, “New aspects
in function spaces, differential and integral operators and nonlinear
analysis, and applications in PDE”, No.GNSF/ST09_23_3100.
c)
01.01.2008 01.01.2011: Georgian
National Science Foundation Grant “Some Topics of Harmonic and Nonlinear
Analysis in Nonstandard Setting with Applications in Differential
Equations” No. GNSF/ST07/3169.
d)
2008, 2009: Grant GNAMPA (Italy),
University of Padova, Italy.
e)
01.01.200701.01.2009: INTAS grant :
“Variable Exponent Analysis”,
Nr.0610000178792.
f)
20062008: Georgian National Science Foundation Grant,
“Nonstandard function spaces and functions with applications to partial
differential equations”, No. GNSF/ST06/3010.
g)
01.09. 200601.09.2008: INTAS grant:
“Function spaces and applications to partial differential equations”, No.
0510000088157.
h)
1998, 20002004, 2006 2009: Georgian President’s Grant for Young
Scientists.
i)
20012002: An INTAS Fellowship grant for
Young Scientists (Fellowship Reference No YSF 01/18).
j)
1999, 2001: Grant of the Royal Society
(UK).
k)
19992003: Grant of the Georgian Academy
of Sciences No. 1.7.
l)
19971998: J. Soros Grant for Postgraduate Students.
m)
20122014: Integral operators and
boundary value problems in new function spaces; new aspects in Fourier and
wavelet theories. Shota Rustaveli
National Science Foundation Grant (contract No. D/1323).
n)
20132015: Modern Problem s of Harmonic
Approximation and Integral Operator Theories in New Function Spaces;
Applications to the Boundary Value Problems (contract number 31/47)
12. Awards:
a)
17.10.2012:
Andrea Razmadze Prize of the Georgian
National
Academy of Sciences.
b) 12.10.2009: Award of the Georgian Mathematical Union for
young scientists.
c) 2002: Award
of the Georgian Mathematical
Union for the best scientific works among young mathematicians.
d)
2000:
Euler Premium for young scientists established by the
German Mathematical Association (Germany).
e) 1995:
Diploma for winning the first place in the students'
republican scientifictechnological conference.
13.
Participation in Conferences, Congresses, Schools etc:

"Multilinear Integral Operators
in Weighted Function Spaces", II Advanced Courses of TICMI in Applied
Mathematics, 2829 SEPTEMBER, 2015, TBILISI, Georgia, I. Vekua Institute of
Applied Mathematics of I. Javakhishvili Tbilisi State University.

"Multilinear Integral Operators
in Some Nonstandard Weighted Function Spaces" (Plenary Speaker),
SwedishGeorgian Conference in Analysis and Dynamical Systems, July 1522,
Tbilisi, Georgia.

"Fractional integral operators
between Banach function lattices" (Invited Speaker), International
Workshop on Operator Theory and Applications (IWOTA 2015), July 610,
Tbilisi, Georgia.

"Onesided operators in grand
variable exponent Lebesgue spaces", Joint International Meeting of the
American, European and Portuguese Mathematical Societies (AMS, EMS and SPM,
respectively), June 1013, 2015, Porto, Portugal.

"SemiPlenary
talk)’Multisublinear maximal operators in Banach Function Lattices", V
Annual International Conference of the Georgian Mathematical Union’’,
September 812, 2014, (book of Abstracts, P. 47).

"Twoweight criteria for Riesz
potentials on cones of radially decreasing functions", Caucasian Mathematics
Conference (CMC I), Tbilisi, September 56, 2014 (book of abstracts, p.
135).

"Weighted
criteria for multilinear fractional integrals",
International Congress of Mathematicians (ICM
2014)", August 1321, Seoul, Korea.

"Interior estimates and regularity
of solutions for elliptic equations in Nondivergence with VMO Coefficients" (Plenary
talk),
IV International Conference of the Georgian Mathematical Union Dedicated to
Academician Victor Kupradze (1903 – 1985) on the
occasion of 110th anniversary of his birthday and to the Georgian
Mathematical union on the occasion of 90 year from founding,
TbilisiBatumi, September 915, 2013.

"Boundedness
and compactness criteria for positive kernel operators in
variable exponent Lebesgue spaces", International ISAAC 9th Congress,
59 August, 2013, Krakow, Poland.

"Integral
operators in new function spaces: one and two weight problems’, International
Conference ‘’Function Spaces X’’, July 914, Poznan, Poland.

"Oneweighted
and trace inequalities criteria for fractional integrals in grand Lebesgue
spaces", 8^{th}International
Conference on 'Function Spaces, Differential Operators, and Nonlinear Analysis'
(FSDONA 2011), September 1824,
2011, Tabarz/Thuringia, Germany.

"Integral operators
in new function spaces" (Plenary talk),
International
Conference CONTINUUM MECHANICS AND
RELATED PROBLEMS OF ANALYSIS dedicated to the N. Muskhelishvili 120th birthday
anniversary, September 10–14, Tbilisi, Georgia Tbilisi, September 914, 2011.

"Potential
and singular operators in grand Lebesgue and Morrey spaces"
(Invited Speaker),
5th World Conference on 21st Century
Mathematics, Abdus Salam School of Mathematical Sciences, GC University,
Lahore, Pakistan, 913 February, 2011.”

"On
the Hardy Inequality", Young Researchers
First International Camp, July 2531, 2010, Bakuriani, Georgia.

"Weighted
estimates for operators of harmonic analysis in nonstandard Lebesgue spaces
and some applications",
XXXConvegnoNazionale di
AnalisiArmonica, Gargnano, 711 giugno 2010, Italia.

"Onesided
potentials with multiple kernels on cones of monotonic functions. One and two
weight criteria" (Invited Speaker).
International Conference on Mathematical Inequalities and Applications
(MIA), School of Mathematical Sciences,
(GC University), March 713, 2010,Lahore, Pakistan.

"Maximal
functions and potentials in Morrey spaces associated with grand Lebesgue
spaces", BatumiKutaisi, Georgia, 912 October, 2009.

"Potentials
and singular integrals in Morrey spaces"
(Invited
Speaker), 4th World Conference on
21^{st} Century Mathematics, Abdus Salam School of Mathematical
Sciences, Lahore, Pakistan, March 48, 2009.

"Trace inequalities for fractional maximal and
potential operators in L^{p(x)} spaces", International Workshop in Variable Exponent Analysis and Related
Topics, Tbilisi, Georgia,
September 25, 2008.

"Boundedness
of onesided operators in variable exponent Lebesgue spaces", Workshop and
Conference In Function Spaces, Differential Operators and Nonlinear Analysis,
Helsinki, Finland, August 2229, 2008.

(a)
"Onesided operators in Lebesgue spaces vith variable exponent"; (b)
"Twoweight estimates for generalized potentials, maximal functions and
singular integrals in Variable exponent Lebesgue spaces". International
Conference “Weight Estimates of Differential and Integral Operators and Their Applications”, Astana, Kazakhstan, September 35, 2007.

"On
the boundedness of onesided maximal
functions and singular integrals in
Lebesgue spaces with variable exponent", 6th International ISAAC Congress, Ankara,
Turkey, 1318 August, 2007.

"Twoweight
estimates for maximal functions, potentials and singular integrals in variable
exponent Lebesgue spaces", International
Workshop in Variable Exponent Analysis, Baku, Azerbaijan, May 1418, 2007.

"Twoweight
estimates for potentials and singular integrals in variable Lebesgue spaces",
3^{rd} International Conference on 21^{st} Century Mathematics,
2007, School of Mathematical Sciences and National Centre for Mathematics, GC
University, Lahore, Pakistan, March
47, 2007.

"Twoweight
estimates for strong fractional maximal functions and potentials with multiple
kernels and application in weighted Strichartz estimates for nonhomogenous
wave equations" . IV Congress of Georgian Mathematicians, Tbilisi, Georgia,
November 1416, 2005.

"Twoweight
estimates for potential operators with multiple kernels and some applications
in the solvability of nonlinear wave equations". International Workshop and School Function
Spaces, Integral Operators and Applications (Coordinators: V. Kokilashvili and A. Meskhi)
Tbilisi, Georgia, August 31 September
4, 2005.

"Stime a due pesi per
funzionimassimaliforti e potenziali con nuclei multipli". XXV ConvegnoNazionale di AnalisiArmonica
(Italia), Universita` di Bologna, Dipartimento di Matematica, 69 ,aprile
2005, Organizzatore: Nicola Arcozzi.

"Fractional
integrals on nonhomogeneous spaces ",
European Mathematical Society Conference "Analysis on Metric
Measure Spaces ", Supported by: Sixth Framework Programme of the European
Commission, UNESCO  ROSTE, Venice,
Banach Center, Bedlewo , Poland, July 15  23, 2004.

"Fractional
integrals on nonhomogeneous spaces ",
7th International Conference on
Harmonic Analysis and Partial Differential Equations, El Escorial, Madrid
(Spain) June 2125, 2004.

"Criteri
di limitatezza per operatoripotenziali con nuclei prodotto" XXIVConvegnoNazionale di AnalisiArmonica
(Italia) , SestriLevante, 29 Marzo  1 Aprile, 2004.

"On
the boundedness and compactness for onesided potentials on the Lebesgue spaces
with variable exponent'', Summer School
in HARMONIC ANALYSIS in the framework of
HARP (Harmonic Analysis and Related Problems), Pisa, Italy, September 113,
2003.

"On
a trace inequality for the
RiemannLiouville operator in Lebesgue spaces with variable exponent.",
International Workshop Modern Aspects in Function Spaces, Differential
Operators and Nonlinear Analysis, Tbilisi, Georgia. Coordinators: V. Kokilashvili, A. Meskhiand
S. Samko,
September 813, 2003.

"On a meassure of noncompactness for the
HardyLittlewood maximal Functions and CalderonZygmund singular integrals",
ISAAC Conference on Complex Analysis,
Differential Equations and Related Topics,
Yerevan, Armenia, Seprember
1721, 2002.

"On
a measure of noncompactness formaximal functions", Congress of Georgian
Mathematicians, Tbilisi, Georgia, 1113 October, 2001.

"On
a trace inequality for onesided potentials and applications to the solvability
of nonlinear integral equations". Simposium in Differential Equations and
Mathematical Physics Dedicated to Academician N. Muskhelishvili, A. Razmadze
Mathematical Institute, Tbilisi, Georgia,
July 2325, 2001.

"Boundedness
and compactness criteria for integral operators with positive kernels",
Scientific Conference Dedicated to Academician I. Vekua, Sukhumi Branch of I.
Djavakhishvili State University, Tbilisi, Georgia, April 21, 2001.

"Weighted
problems for higher dimensional singular integrals via Clifford analysis", NATO
Advanced Workshop " Clifford Analysis and its Applications",
Prague, Czech Republic, October 30 November 3,
2000.

"Boundedness
and compactness weighted criteria for the operators with positive
kernels". European Congress for
Mathematics, Barcelona, July 1014, 2000.

"Boundedness and compactness weighted criteria for kernel integral
operators", International Symposium
in Advanced Course on Function Spaces and Applications, Tbilisi, Georgia, September 610, 1999.

"Twoweight
boundedness and compactness criteria for onesided maximal functions and
potentials", The first International Junior Conference in Mathematical
Analysis, A. Razmadze Mathematical Institute, Tbilisi, Georgia, April 30 May
1, 1998.

"Weighted
Inequalities for the Riemann Liouvlille and Weyl operators defined on
SHT", International Congress of Mathematicians, Berlin, Germany, August
1827, 1998.

"Boundedness
and compactness criteria for the Riemann Liouville and Weyl
transforms", International Conference
in Nonlinear Analysis, Function Spaces and Applications 6, Prague, Czech
Republic, May 31 June 6, 1998.

"Twoweight
estimates for singular integrals",
Congress of Georgian Mathematicians, Tbilisi, Georgia, September, 1997.
14.
Scientific and Academic Visits

2016
(January 25 February 25), San Diego State University, USA.

2014 (October 716) Adam Mickiewicz University of Poznan, Poland.

2013 (June 23July 2) Adam Mickiewicz University of Poznan,
Poland.

2010
(September 30December 30) University of Padova, Italy

2010
(May 15June 15) University of Padova, Italy

2009 (April 15 June 14) University of
Padova, Italy.

2008
(January 14 March 12) University of Padova, Italy.

2006
(November 25 December 5) University of Pisa, Italy.

2006
(July 2 July 15), University of Sussex, UK.

2005
(June 1 September 1), Department of Mathematics, University of Pisa, Italy.

2005
(January 23 February 4), University of Sussex (UK).

2004
(November), University of Naples, department of mathematics (Italy).

2002
(JuneJuly), University of Sussex (UK).

2001
(April), University of Sussex (UK);

1999
(March), University of Sussex, Cardiff University (UK);

1998
(June 1 7), Mathematical Institute of the Czech
Republic.
15.
Talks in Seminars:

3.01.2016. ''On Some Mapping Properties of Multilinear Integral
Operators'', San Diego State University, USA.

14.10.2014, Multisublinear maximal type
operators in Banach function lattices’’ , Adam Mickiewicz University of Poznan,
Faculty of Mathematics and Computer Sciences'' ( Head of the Seminar, Professor
M. Mastylo).

25.06.2013, ‘’Weighted criteria for multilinear
fractional integrals’’, Adam Mickiewicz University of Poznan, Faculty of
Mathematics and Computer Sciences'' ( Head of the Seminar, Professor M. Mastylo).

31.06.2010.
“Fractional and singular integrals in grand Lebesgue spaces”,
Department of Mathematics, University of
Padova, Italy, (Head of the Seminar Prof. Massimo Lanza de Cristoforis).

11.12.2006. “Criteri per la
limitatezzadeipotenzialiedintegralisingolarineglispazi di Lebesgue con
l’esponentevariabile”. University of Pisa, Italy, (Head of the Seminar Prof.
Vladimir Georgiev).

05.12.2006.
“Twoweight inequalities for potential operators and some
applications”.Department of Mathematics, University of Padova, Italy, (Head of
the Seminar Prof. Massimo Lanza de Cristoforis).

27.05.2005:
"On a trace inequality for potentials and applications in the solvability
of nonlinear integral equations and the spectral theory of integral
operators", Department of Mathematics, University of Pisa, Italy, (Head
of the Seminar Prof. V. Georgiev).

11.11.2004:"Twoweight
estimates for multiple Hardytype transforms and some applications",
ScuolanormaleSuperiore, Italy (Head of the Seminar Prof. Fulvio Ricci).

12.01.2004,
26.01.2004: Twoweight inequalities for potential operators and some
applications, ScuolaNormaleSuperiore, Pisa, Italy, (Head of the Seminar Prof.
Fulvio Ricci).

30.03.
1999: " Boundedness and compactness criteria for onesided
potentials", University of Wales, UK, (Head of the Seminar Prof.
W.D.Evans).

11.06.1998: "Boundedness and compactness
criteria for the RiemannLiouville Transforms", Mathematical Institute of
the Academy of Sciences of Czech Republic, (Head of the Seminar Professor
AloisKufner).
16.
Teaching:
a)
10.2010
12.2010: University of Padova (Courses: “Mathematical Analysis 2”; “Function Theory 2”; “Interpolation
theory and applications in Sobolev
spaces and spaces with fractional regularity”);
b)
10.2010
12.2010: School of Galileo Galilei, University of
Padova, Italy (Course: “Measure Theory and Probability 1”).
c)
28.09.2009up
to now: Georgian Technical University (Courses: “Linear Algebra and Analytic
Geometry”; “Mathematical Analysis 1”).
d)
15.04.2009
15.06.2009: School of Galileo Galilei, University of
Padova, Italy (Course “Fourier Analysis”).
e)
15.01.2008
14.03.2008: School of Galileo Galilei,
University of Padova, Italy (Course “Inequalities of Real Analysis”).
f)
2006
up to now: School of Mathematical Sciences, GC University, Lahore,
Pakistan (Courses: “Functional Analysis”, “Measure Theory”, “Complex
Analysis”).
g)
09.2005 12.2005: International Black Sea
University, Tbilisi, Georgia (Course of Calculus for the first year students of
the Faculty of Economics and Administrative Sciences).
h)
20012003:
Tbilisi State University, Georgia,
(Course of Ordinary Differential Equations, Faculty of Differential
Equations).
i)
19961998:
Technical University of Georgia (Courses of Mathematical Analysis, Theory of
Functions, Functional Analysis for the Students of the Faculty of Informatics
and Control Systems).
j)
Experience in Working with PhD Students.
17.
List of Those Specialists Who Can Evaluate A. Meskhi’s Research and Teaching Abilities (Possible Referees):
1.
Professor
Vakhtang Kokilashvili. Address: A. Razmadze Mathematical Institute of the
Georgian Academy of Sciences, 1. M. Aleksidze Str. 0193 Tbilisi, Georgia. Tel
(00) 995 32 233 35 12; Email: kokil@rmi.acnet.ge
2.
Professor
David E. Edmunds, Address: School of Mathematics, Cardiff University,
Senghennydd Road, Cardiff CF24 4YH, U.K. email: DavidEEdmunds@aol.com
3.
Professor
Stefan Samko, Faculdade de Ciencias e Tecnologia, University do Algarve, Campus
de Gambelas, 8005139 Faro, Portugal, Tel: (351)289800900. ext. 7667;
email: ssamko@ualg.pt
4.
Professor
Vladimir Georgiev, Address: Department of Mathematics, University of Pisa,
56127, Pisa, Largo Bruno Pontecorvo 5, Italy; Tel. (00)390502213301,
Email: georgiev@dm.unipi.it
5.
5.
Professor W.D. Evans, Address: Cardiff School of Mathematics, Cardiff
University, 23 Senghennydd Road, Cardiff CF24 4AG, WALES, UK, Tel. (+44)
029 2087 4827 ;
6.
Fax:
(+44) 029 2087 4199, email: EvansWD@cf.ac.uk
7.
Professor
Fulvio Ricci, Scuola Normale Superiore, Piazza dei Cavallieri 7, 56126 Pisa,
Italy, Telephone: +39050509257, email: fricci@sns.it.
8.
Professor
Alberto Fiorenza, Dipartimento di Costruzioni e Metodi Matematici in
Architettura, Universita' di Napoli Federico II, via Monteoliveto, 3, 80134 
NAPOLI (NA) – ITALY, email: fiorenza@unina.it
18.
PhD Students of A. Meskhi:
1.
GhulamMurtaza,
Title of the thesis: “Twoweight criteria
for potentials with product kernels on the cone of nonincreasing functions”’,
Abdus Salam School of Mathematical Sciences, Lahore, 10.02.2012.
2.
Muhammad
Sarwar. Title of the thesis: “Maximal and potential operators in weighted Lebesgue spaces with
nonstandard growth”, Abdus
Salam School of Mathematical Sciences,
Lahore, 12.10.2011.
3.
Usman
Ashraf. Title of the thesis: “On trace inequalities and compactness for
potentialtype operators." Abdus Salam School of Mathematical Sciences,
Lahore, 2009.
4.
Muhammad Asif, Title of
the thesis: “On the boundedness and measure of
noncompactness for maximal and potential operators”, Abdus Salam School
of Mathematical Sciences, Lahore, 2009.
5.
M. A. Zaighum,
Title of the thesis: “Kernel operators in some new function spaces”, Abdus Salam School of Mathematical Sciences, Lahore, 2014.
19. Editorial Activities
a)
Editor in Chief of the International Journal ‘‘Transactions of A. Razmadze
Mathematical Institute’’ (Elsevier);
b) Member of the Editorial Board of the International Journal
‘‘Universitas Scientiarum’’ (Columbia);
c) Member of the Advisory Board of the International Journal
‘’Journal of the Prime Research in Mathematics’’ (Abdus Salam School of
Mathematical Sciences, Lahore);
d) Member of the Editorial Board of the of the International
Journal ‘’Journal of Mathematical Inequalities’’ (JMI) (Croatia).
e) Associate Editor of ‘’Journal of Inequalities and
Applications’’ (Springer).
f) Member of the Editorial Board of ‘’Tbilisi
Mathematical Journal’’ (Georgia).
g) Member of the Editorial Board of ‘’ Commenatationes
Mathematicae’’ (Poland).
20. Membership:
a) Member of the American Mathematical
Society;
b) Member of the Georgian Mathematical
Union.
21. Other Information
a) Included in the list of ‘’Top 100
Professionals’’ by the Cambridge Bibliographic Center (2015);
b) Included in the list of ‘’2000 Intellectuals
of the 21st Centary’’ by the Cambridge Bibliographic Center (2015);
c) Included in ‘’Who is who’’ bibliographic
center (2015).
List
of Publications of A. Meskhi
Monographs:
1.
D.
E. Edmunds, V. Kokilashvili and A.
Meskhi, Bounded and Compact Integral
Operators, Kluwer Academic Publishers, Dordrecht, Boston, London, 2002.
2.
A.Meskhi, Measure of
Noncompactness for Integral Operators in Weighted Lebesgue Spaces. Nova Science
Publishers, New York, 2009.
3.
V.
Kokilashvili, A. Meskhi and L. E.
Persson, Weighted Norm Inequalities for
Integral Transforms with Product Kernels, Nova Science Publishers, New
York, 2010.
4.
V. Kokilashvili, A. Meskhi, S.
Samko, and H. Rafeiro, Integral Operators in Nonstandard Function
Spaces. Vol. I. Variable Exponent Lebesgue
and Amalgam Spaces. Birkhäuser, 2015, pp. 1586.
5.
V.
Kokilashvili, A.
Meskhi, S. Samko, and
H. Rafeiro, Integral
Operators in Nonstandard Function Spaces. Vol. II. Variable Exponent Hölder, MorreyCampanato and
Grand spaces. Birkhäuser, 2016, pp. 5871009.
Papers
(by the symbol * it is denoted papers published in journals with ImpactFactor)
1.
Twoweight
inequalities for singular integrals on Heisenberg groups. Bull. Acad. Sci. Georgia 153(1996), No. 1, 3436.
2.
Two
weight inequalities for potentials on homogeneous groups. Bull. Acad.
Sci. Georgia 154(1996), No.
3, 353355.
3.
Twoweight
inequalities for the Hardy operator on the Lorentz spaces defined on
homogeneous groups. Proc. A. Razmadze Math. Inst. 112(1997), 138140 (with V.
Kokilashvili).
4.
Twoweight
inequalities for singular integrals on the Lorentz spaces defined on
homogeneous groups. Proc. A. Razmadze Math. Inst. 112(1997), 143145 (with V.
Kokilashvili).
5.
Twoweight
inequalities for potentials on the Lorentz spaces defined on homogeneous
groups. Proc. A. Razmadze Math. Inst. 112(1997), 148150.
6.
Twoweight
inequalities for Hardytype transforms and singular integrals defined on
homogeneous type spaces. Proc. A. Razmadze Math. Inst. 114(1997),
119123 (with V.Kokilashvili).
7.
* Twoweight estimation for singular integrals defined on
homogeneous groups. (Russian) Doklady Academy Nauk RAN 354(1997) No. 3, 301303. English transl. in Doklady Mathematics 55(1997), No. 3, 362364 (with V. Kokilashvili).
8.
* Weighted inequalities for the Hilbert transform and
multipliers of Fourier transforms. J.
Inequal. Appl. 1(1997), No. 3, 239 252 (with V. Kokilashvili).
9.
Two
weight inequalities for singular integrals defined on homogeneous groups. Proc. A. Razmadze Math. Inst. Georgian Acad.
Sci. 112(1997), 5790 (with
V. Kokilashvili).
10.
Twoweight
inequalities for potentials defined on homogeneous groups. Proc. A. Razmadze
Math. Inst. 112(1997), 91
111.
11.
Koosis
type theorems for singular integrals and potentials defined on homogeneous
groups. Proc. A. Razmadze Math. Inst.
114(1997), 59 70.
12.
Boundedness
and compactness weighted criteria for RiemannLiouville and onesided maximal
operators. Proc. A. Razmadze Math. Inst. 117(1998),126128.
13.
Weighted
inequalities for RiemannLiouville transform, Proc. A. Razmadze Math. Inst.
117(1998), 151153.
14.
* Solution of some weight problems for the RiemannLiouville
and Weyl operators. Georgian Math. J.
5(1998), No. 6, 265274.
15.
Twoweight
inequalities for a discrete Hilbert transform.
Proc. A. Razmadze Math. Inst. 116(1998), 107122. (with I.
Gabisonija).
16.
Twoweight
inequalities for a discrete Hardy operators and Hilbert transform. Bull.
Acad. Sci. Georgia 158(1998), No. 2, 191193 (with I. Gabisonija).
17.
Boundedness
and compactness of Hardytype operators in Banach function spaces. Proc. A.
Razmadze Math. Inst. 117(1998),
730 (with D. E. Edmunds and V. Kokilashvili).
18.
* Twoweight inequalities for integral operators in Lorentz
spaces defined on homogeneous groups. Georgian Math. J.
6(1999), No. 1, 65 82 (with V.
Kokilashvili).
19.
Boundedness
and compactness criteria for the generalized RiemannLiouville operator.
Proc. A. Razmadze Math. Inst. 121(1999), 161162.
20.
On
the boundedness and compactness of ball fractional integral operators. Fract. Calc. Appl. Anal. 3 (2000), No. 1,
1330.
21.
On
the measure of noncompactness and singular numbers for the Volterra integral
operators. Proc. A. Razmadze Math. Inst.
123(2000), 162165.
22.
Boundedness
and compactness criteria for some classical operators. Proc. Int. Conf.
"Function Spaces V", Poznan, Poland, August 28 September 3, 1998, Marcel Dekker Publ, 273296, Marcell
Dekker, New York, Bazel, 2000 (with V. Kokilashvili).
23.
On
the boundedness and compactness of generalized truncated potentials. In: Bull. of Tbilisi Int. Centre of Math. and
Inform. Vol. 4, 2831, 2000 (with V. Kokilashvili).
24.
Weighted
problems for higher dimensional singular integrals via Clifford analysis, Proceedings of the NATO ARW " Clifford
Analysis and its Applications" Held in Prague, October. 30 November
3, 2000, F. Brackx, J.S.R. Chisholm and V. Soucek (eds.), 247253, Kluwer
Academic Publishers, Dordrecht (The Netherlands), 2001 (with V. Kokilashvili).
25.
* Twoweight
estimates for singular integrals defined on spaces of homogeneous type. Canadian
J. Math. 52(2000), No. 3, 468502 (with D. E.
Edmunds and V. Kokilashvili).
26.
Norms
of positive operators on some cones of functions defined on measure
spaces. Proc. A. Razmadze Math. Inst. 122(2000),
5978 (with V. Kokilashvili).
27.
Criteria
of the boundedness and compactness for generalized onesided potentials. Real
Anal. Exchange 26(2000/2001),
No. 1, 217 236.
28.
* Criteria for the boundedness and compactness of operators with
powerlogarithmic kernels. Analysis Math. 27(2001), No. 2, 173 185 (with V. Kokilashvili).
29.
On
the boundedness and compactness criteria for the RiemannLiouville type discrete
operator. Proc. A. Razmadze Math. Inst. 126(2001),
117119.
30.
* Criteria for the boundedness and compactness of integral
transforms with positive kernels, Proc. Edinburgh
Math. Soc. 44(2001), 267284.
31.
* Weight inequalities for singular integrals defined on
spaces of homogeneous and nonhomogeneous type. Georgian Math. J. 8(2001), No. 1, 3359 (with D. E.
Edmunds and V. Kokilahsvili).
32.
* Asymptotic behavior of singular and entropy numbers for
some RiemannLiouville type operators. Georgian
Math. J. 8(2001), No. 2, 323 332.
33.
* On a trace inequality for onesided potentials and
applications to the solvability of nonlinear integral equations. Georgian Math. J. 8(2001), No. 3. 521536 (with V.
Kokilashvili).
34.
Fractional
integrals on measure spaces, Fract. Calc. Appl. Anal. 4(2001), No.1. 124 ( With V.
Kokilashvili).
35.
* On the singular
numbers for some integral operators. Revista Mat. Compl. 14(2001), No. 2, 379393.
36.
*
Boundedness
and compactness criteria for the generalized truncated potentials (Russian), Proc. Steklov Math. Inst. RAN 232(2001), 164178. Engl. Transl. In: Proc. Steklov Inst. Math. 232(2001) (with V. Kokilashvili).
37.
On
a measure of noncompactness for the Riesz transforms. Proc. A. Razmadze Math. Inst. 129
(2002), 156157.
38.
* On Fourier
multipliers in weighted TriebelLizorkin spaces, J. Inequal. Appl. 7(2002), No. 4, 555591 (with. D.E.Edmunds and V.
Kokilashvili) .
39.
* Potentialtype operators in $L^{p(x)}$ spaces, Z.
Anal. Anwend. 21(2002), No. 3, 681690 (with D.E.
Edmunds).
40.
Weight
inequalities for onesided potentials for critical weights. Fract. Calc. Appl.
Anal. 5(2002), No.3, 255265 (with V. Kokilashvili).
41.
* On
a measure of noncompactness for maximal operators. Math. Nachr. 254255 (2003), 97106 (with D.E.
Edmunds).
42.
* On
a measure of noncompactness for singular integrals. J.
Funct. Spaces Appl. 1(2003), No.1, 3543.
43.
On
the inversion and characterization of the Riesz potentials in the weighted
Lebesgue spaces. Mem. Differential
Equation Math. Phys. 29(2003),
3145 (with V. Kokilashvili and S. Samko).
44.
On
a trace inequality for onesided potentials with multiple kernels. Frac. Calc.
Appl. Anal. 6(2003), No.
4, 461 472 (with V. Kokilashvili).
45.
* A
trace inequality for generalized potentials in Lebesgue spaces with variable
exponent. J. Funct. Spaces Appl. 2(2004),
No. 1, 5569 (with D. E. Edmunds and V. Kokilashvili).
46.
On
twoweight inequalities for multiple Hardytype
operators. Proc. A. Razmadze Math.
Inst. 136(2004), 149153.
47.
On
twoweight estimates for strong fractional maximal functions and potentials
with multiple kernels. Proc. A. Razmadze Math. Inst. 137(2005), 135140 (with V. Kokilashvili).
48.
* On the boundedness
and compactness of the weighted Hardy operators in $L^{p(x)}$ spaces. Georgian Math. J. 12(2005), No. 1, 2744 (with D. E.
Edmunds and V. Kokilashvili).
49.
Strong
and iterated maximal functions, and applications to the mean summability of the
double trigonometric Fourier series. Proc. A. Razmadze Math. Inst. 139(2005), 132136 (with V. Kokilashvili and Ts. Tsanava).
50.
On
a weighted Strichartz estimate for inhomogeneous wave equations. Proc. A. Razmadze Math. Inst. 139(2005),
9699 (with V. Georgiev).
51.
* On onesided
potentials with multiple kernels. Integral
Transf. Spec. Funct. 16 (2005), No. 8, 669683.(with V. Kokilashvili).
52.
* On some twoweight
inequalities for fractional integrals on nonhomogeneous spaces, Z. Anal. Angewend. 24(2005), No. 4, 871885 (with V.
Kokilashvili).
53.
* A note on
twoweight inequalities for multiple Hardytype operators, J. Funct. Spaces Appl. 3(2005), 223237.
54.
Twoweighted
criteria for integral transforms with multiple kernels, In: Proceedings of Conference on the Occasion of
the 70 Anniversary of Professor Zbigniew Ciesielski, Bedlewo, 20  24 September, 2004, Institute of Mathematics, Polish Academy of
Sciences, Banach Center Publications 72(2006), 119140 (with V.
Kokilashvili).
55.
Twoweight
estimates in $L^{p(\cdot)}$ spaces for classical integral operators and
applications to the norm summability of Fourier trigonometric series. Proc. A. Razmadze Math. Inst. 142(2006), 123128 (with D. Edmunds and
V. Kokilashvili).
56.
* On a measure of
noncompactness for some classical operators. Acta Math. Sinica (Eng.
Series) 22(6)(2006), 18471862 (with D. E. Edmunds and A. Fiorenza).
57.
On
a class of bounded and compact higher dimensional kernel operators. Proc. A. Razmadze Math. Inst. 144(2007), 121125 (with U. Ashraf and
M. Asif).
58.
On
onesided operators in variable exponent Lebesgue spaces. Proc. A. Razmadze Math. Inst. 144(2007),
126131 (with D. E. Edmunds and V. Kokilashvili).
59.
On
twoweight criteria for maximal function in
$L^{p(x)}$ spaces defined on an interval. Proc.
A. Razmadze Math. Inst. 145(2007),
100102 (with V. Kokilashvili).
60.
Twoweight
Estimates for Strong Maximal Functions, Potentials and Singular Integrals with
Multiple Kernels, Proceedings of
Conference on the Occasion of the 70 Anniversary of Professor Ryskul Oinarov,
Astana, Kazakhstan, September 35, 2007. Published in “Evrazii’skii’ Matematicheskii’ Zhurnal” No. 2, 2007, 3146 (with V. Kokilashvili).
61.
* Twoweight estimates for singular and strongly singular
integral operators. Acta Math. Hungar.
116 (2007), No. 12, 125 (with V. Kokilashvili and N. Lyall).
62.
* Weighted criteria for generalized maximal functions and
potentials in Lebesgue spaces with variable exponent. Int.
Trans. Spec. Funct. 18 (2007), No. 9, 609628 (with V. Kokilashvili).
63.
On
the maximal and Fourier operators in weighted Lebesgue spaces with variable
exponent, Proc. A. Razmadze Math. Inst.
146 (2008), 120123 (with V.
Kokilashvili).
64.
Maximal
and potential operators in variable Morrey spaces defined on nonhomogeneous
spaces. Bull. Georgian National Acad.
Sci. 2(2008), No. 3, 1821 (with V. Kokilashvili).
65.
One
and two weight estimates for onesided potentials in $L^{p(x)}$ spaces, Proc. A. Razmadze Math. Inst. 148(2008),
126–133 (with V. Kokilashvili and M. Sarwar).
66.
* On the essential norm for the Hilbert transforms in
$L^{p(x)}$ spaces, Georgian Math. J. 15(2008), No. 2, 208223 (with M. Asif).
67.
Boundedness
of maximal and singular operators in Morrey spaces with variable exponent, Armenian J. Math. 1(2008), No.1, 1828 (with
V. Kokilashvili).
68.
* Weighted estimates of a measure of noncompactness for
maximal and potential operators. J.
Inequal. Appl. 2008, Art. ID 697407, 19
pages (with M. Asif).
69.
* Onesided operators
in $L^{p(x)}$ spaces. Math. Nachr. 281(2008),
No. 11, 1525–1548 (with D. E. Edmunds and V. Kokilashvili).
70.
* Twoweight estimates in
$L^{p(\cdot)}$ spaces with applications to Fourier series. Houston Journal of Mathematics 35(2009) , No. 2, 665689 (with D. E.
Edmunds and V. Kokilashvili).
71.
* Boundedness and compactness
of positive integral operators on cones of homogeneous groups. Positivity 13 (2009), no. 3, 497–518. DOI
10.1007/s1111700822178, 497518 (with
U. Ashraf and M. Asif).
72.
Maximal
functions and singular integrals in Morrey spaces associated with grand
Lebesgue spaces. Proc. A. Razmadze Math.
Inst. 151(2009), 139143.
73.
Twoweight
estimates for maximal, potential and singular operators in $L^{p(x)}$ spaces. Proc.
A. Razmadze Math. Inst. 149(2009),
122125 (with V. Kokilashvili).
74.
Twoweight
criteria for onesided strong fractional maximal functions. Proc. A. Razmadze Math. Inst. 149(2009), 118121. (with V.
Kokilashvili).
75.
* Boundedness
criteria for maximal functions and potentials on the halfspace in
weighted Lebesgue spaces with variable
exponents. Integr. Transf. Spec. Func.
20(2009), No. 11, 805819 (with M.
Asif and
V. Kokilashvili).
76.
* Twoweight
estimates for strong fractional maximal functions and potentials with multiple
kernels. J. Korean Math. Soc. 46 (2009), No. 3, 523–550 (with V. Kokilashvili).
77.
* Morrey spaces and
fractional integral operators. Expo.
Math. 27(2009), 227239 (with Eridani and V. Kokilashvili).
78.
* A
note on the boundedness of the Hilbert transform in weighted grand Lebesgue
spaces, Georgian Math. J. 16 (2009), No. 3, 547551 (with V. Kokilashvili).
79.
* Maximal
functions and potentials in variable exponent Morrey spaces with nondoubling
measure. Complex Variables and Elliptic
Equations 55 (2010), No. 8, 923936
(with V. Kokilashvili).
80.
Twoweight
criteria for potentials with product kernels on cones of decreasing functions. Proc. A. Razmadze Math. Inst. 152(2010), 144153 (with G. Murtaza and
M. Sarwar).
81.
Weight
characterization of the trace inequality for the generalized RiemannLiouville
transform in $L^{p(x)}$ spaces. Math.
Ineq. Appl. 13(2010), No.1,
6381 (with U. Ashraf and V. Kokilashvili).
82.
One
and two weight estimates for onesided
operators in $L^{p(\cdot)}$ spaces. Eurasian
Math. J. 1(2010), No. 1,
73110 (with V. Kokilashvili and M.
Sarwar).
83.
* Potential
operators in variable exponent Lebesgue spaces:
Two–weight estimates. J. Inequal.
Appl. 2010, Article ID 329571,
27 pages. doi: 10.1155/2010/329571 (with V. Kokilashvili and M. Sarwar).
84.
* Weighted criteria for onesided potentials with product
kernels on cones of decreasing functions. Math.
Ineq. Appl. 14(2011), No. 3,
693–708 (with G. Murtaza and M. Sarwar).
85.
Maximal
functions, potentials and singular integrals in grand Morrey spaces. Complex Variables and Elliptic Equations
56(2011), Nos. 10–11, 1003–1019.
86.
Twoweight inequalities for fractional maximal functions
and singular integrals in $L^{p(\cdot)}$ spaces. J. Math. Sci. (Springer, N.Y.) 173(2011),
No. 6, 13–28 (with V. Kokilashvili).
87.
Weighted
criteria for the Hardy transforms under the $B_p$ condition in grand Lebesgue
spaces and some applications. J. Math.
Sci. (Springer, N.Y.) 178(2011),
No. 6, 622636.
88.
* Potential operators on cones of nonincreasing functions. J. Funct. Spaces Appl. 2012, Article
ID 474681, 26 pages, 2012. doi:10.1155/2012/474681 (with G. Murtaza).
89.
Twoweighted
norm inequalities for the double Hardy transforms and strong fractional maximal
functions in variable exponent Lebesgue spaces, Operator Theory: Advances and Applications 219, B. M. Brown, J. Lang and I. G. Wood (Editors), Spectral
Theory, Function Spaces and Applications, New Techniques and Recent Trends,
Springer Basel AG, 2012, pp.
105124 (with V. Kokilashvili).
90.
Potentials
with product kernels in grand Lebesgue spaces. Proc. A. Razmadze Math. Inst. 159
(2012), 158161 (with V. Kokilashvili).
91.
* On
the boundedness of product kernel operators with measures. Georgian Math. J. 19(2012),
No. 3, 533–557,
DOI: 10.1515/gmj20120020 (with
M. A. Zaighum).
92.
* Trace
inequalities for integral operators with fractional order in grand Lebesgue
spaces, Studia Math. 210 (2012), 159176, DOI:
10.4064/sm21024 (with V. Kokilashvili).
93.
Weight
characterization of the boundedness for the RiemannLiouville discrete
transform. J. Prime Res. Math.
(accepted for publication) (with G. Murtaza).
94.
* Riesz type potential operators in generalized grand Morrey
spaces. Georgian Math. J. 20 (2013), No. 1, 4364 (with V. Kokilashvili and H. Rafeoro).
95.
* Potentials
with product kernels in grand Lebesgue spaces: Oneweight criteria. Lithuanian Math. J. 53
(2013), No.1, 2739' (with V. Kokilashvili).
96.
* Positive
kernel operators in $L^{p(x)}$ spaces. Positivity
17 (2013), No. 4, 11231140; DOI 10.1007/s11117013022599
(with V. Kokilashvili and M. A. Zaighum).
97.
*
Weighted kernel operators in variable exponent amalgam spaces, J. Ineq. Appl.
2013, 2013:173, doi:10.1186/1029242X2013173, pp. 128, (with V. Kokilashvili and M. A. Zaighum).
98.
*
Boundedness of commutators
of singular and potential operators in generalized grand Morrey
spaces and some applications, Studia Math. 217 (2013), No. 2, 159178 (with V. Kokilashvili and H. Rafeiro).
99.
* Twoweight
norm estimates for maximal and CalderónZygmund
operators in variable exponent Lebesgue spaces. Georgian Math. J. 20 (2013), No. 3, 547572 (with V. Kokilashvili
and M. Sarwar).
100.
* Kernel
operators on the upper halfspace:
boundedness and compactness criteria. Turkish J. Math. 38
(2014), No. 1, 119135 (with U. Ashraf and M. Asif).
101.
*
On the boundedness of maximal and potential operators
in amalgam spaces. J.
Math. Inequal. 8 (2014), No. 1, 123152 (with M. A. Zaighum).
102.
*
On the boundedness
of the multilinear fractional integral operators. Nonlinear Analysis,
Theory, Methods and Applications 94
(2014), 142147 (with V. Kokilashvili and M. Mastylo).
103.
*
Estimates for nondivergence elliptic equations with
VMO coefficients in generalized grand Morrey spaces, Complex Variables and Elliptic Equation 59 (2013), No. 8,
11691184 (with
V. Kokilashvili and H. Rafeiro).
104.
* Grand BochnerLebesgue space and its associate space. Journal of Functional Analysis 266 (2014), No. 4, 21252136 (with V. Kokilashvili and H. Rafeiro).
105.
* Twoweight norm estimates for sublinear integral operators in variable exponent Lebesgue spaces, Studia Sci. Math. Hungarica 51
(2014), No. 3, 384406 (with V. Kokilashvili).
106.
Oneweight
weaktype estimates for fractional and singular integrals in grand Lebesgue spaces. Banach Center
Publications 102 (2014), 131142
(with V. Kokilashvili).
107.
Some
fundamental inequalities for trigonometric polynomials in imbeddings
of grand Besov spaces. Proc. A. Razmadze Math. Inst. 165 (2014), 105116 (with V. Kokilashvili).
108.
* Maximal and CalderónZygmund
operators in grand variable exponent Lebesgue spaces.
Georgian Math. J. 21 (2014), No. 4, 447461 (with V. Kokilashvili).
109.
* The multisublinear
maximal type operators in Banach function lattices, J. Math. Anal. Appl. 421 (2015), No. 1, 656668 (with V. Kokilashvili and M. Mastylo).
110.
* Fractional
integral operators between Banach function
lattices, Nonlinear Analysis,
Theory, Methods and Applications 117
(2015) 148158 (with V. Kokilashvili and M. Mastylo).
111.
*
Twoweight norm estimates for multilinear fractional
integrals in classical Lebesgue spaces, Fractional Calculus Applied Analysis
18 (2015), No. 5, 11461163
(with V. Kokilashvili and M. Mastylo).
112.
*
On weighted Bernstein type inequality in grand variable exponent Lebesgue
spaces. Mathematical Inequalities
and Applications
18 (2015), No.3, 991–1002 (with V. Kokilashvili).
113.
* Weighted Kernel Operators in $L^{p(x)}({\Bbb{R}}_+$. J. Math. Ineq.
10 (2016), No. 3, 623–639, DOI: 10.7153/jmi1050 (with M. A. Zaighum).
114.
* Sharp weighted bounds for onesided operators, Georgian Mathematical
Journal (accepted) (with V. Kokilashvili and M. A. Zaighum).
115. *
Weighted extrapolation in IwaniecSbordone spaces. Applications to integral
operators and theory of approximation. Proc. Steklov Inst. Math. 293
(2016), 161–185. Original Russian Text published in Trudy Mat. Inst.
Steklova 293 (2016), 167–192 (with V. Kokilashvili).
116. * Interpolation on variable Morrey spaces defined on quasimetric measure
spaces, J. Functional Analysis 270 (2016), No. 10, 39463961 (with H. Rafeiro and M. A. Zaighum).
117.
Sharp weighted bounds for multiple integral operators, Trans. A. Razmadze
Math. Inst. 170 (2016), 75–90 (with V. Kokilashvili and M. A.
Zaighum).
118. * Multilinear integral operators in weighted grand Lebesgue
spaces, Frac. Calc. Appl. Anal. 19(2016), 691724. (with V. Kokilashvili and M.
Mastylo).
119. Sharp weighted bounds for the Hilbert transform of odd and even
functions, Trans. A. Razmadze Math. Ins. (2016), Doi:
http://dx.doi.org/10.1016/j.trmi.2016.07.005 (with G. Gilles).
120. * The Riemann boundary value problem in the frame of variable
exponent grand Lebesgue spaces, Georgian Math. J. (accepted) (with V.
Kokilashvili and V. Paatashvili).
121. * Sublinear Operators in Generalized Weighted Morrey Spaces,
(Russian) Doklady Acad. Nauk, 470 (2016), No. 5, 502–504.
Translation in: Doklady Mathematics, 94 (2016), No. 2.
122. * Complex interpolation on variable exponent Campanato spaces
of order k, Complex variable and Elliptic Equations (accepted) (with H.
Rafeiro and M. A. Zaighum).