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)11.05.2000-up to now: Senior Researcher  at  A.Razmadze Mathematical Institute, Georgia.

b) 28.09.2009-up to now: Full Professor of the  Technical University of Georgia (Department of Mathematics).

b) 01.2006-up 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. e-mail: 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) 1995-1998 - Post-graduate Student of A. Razmadze  Mathematical Institute  

b) 1990-1995 - 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.) " Two-weight inequalities for singular integrals defined on homogeneous groups".  A. Razmadze Mathematical Institute (Supervisor Prof. V. Kokilashvili).

c) 1995: Master Degree in Mathematics, " Two-weight 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)      18.09.2011-24.09.2013: 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)      01.01.2010-01.01.2013:  Shota Rustaveli National Science Foundation Grant, “New aspects in function spaces, differential and integral operators and non-linear analysis, and applications in PDE”,  No.GNSF/ST09_23_3-100.

c)      01.01.2008- 01.01.2011: Georgian National Science Foundation Grant “Some Topics of Harmonic and Non-linear Analysis in Non-standard Setting with Applications in Differential Equations”  No. GNSF/ST07/3-169.

d)     2008, 2009: Grant GNAMPA (Italy), University of Padova, Italy.

e)      01.01.2007-01.01.2009: INTAS grant : “Variable Exponent Analysis”,  Nr.06-1000017-8792.

f)       2006-2008: Georgian  National Science Foundation Grant, “Nonstandard function spaces and functions with applications to partial differential equations”, No. GNSF/ST06/3-010.

g)      01.09. 2006-01.09.2008: INTAS grant: “Function spaces and applications to partial differential equations”, No. 05-1000008-8157.

h)      1998, 2000-2004, 2006- 2009:  Georgian President’s Grant for Young Scientists.

i)        2001-2002: An INTAS Fellowship grant for Young Scientists (Fellowship Reference No YSF 01/1-8).

j)        1999, 2001: Grant of the Royal Society (UK).

k)      1999-2003: Grant of the Georgian Academy of Sciences No. 1.7.

l)        1997-1998:  J. Soros Grant for Post-graduate Students.

m)    2012-2014:  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/13-23).

n)      2013-2015: 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 Heidelberg Academy of Sciences (Germany).

e)      1995: Diploma for winning the first place in the students' republican scientific-technological conference.

 

13. Participation in Conferences, Congresses, Schools etc:

  1. "Multilinear Integral Operators in Weighted Function Spaces", II Advanced Courses of TICMI in Applied Mathematics, 28-29 SEPTEMBER, 2015, TBILISI, Georgia, I. Vekua Institute of Applied Mathematics of I. Javakhishvili Tbilisi State University.

  2. "Multilinear Integral Operators in Some Non-standard Weighted Function Spaces" (Plenary Speaker), Swedish-Georgian Conference in Analysis and Dynamical Systems,  July 15-22, Tbilisi, Georgia.

  3. "Fractional integral operators between Banach function lattices" (Invited Speaker), International Workshop on Operator Theory and Applications (IWOTA 2015), July 6-10, Tbilisi, Georgia.

  4. "One-sided operators in grand variable exponent Lebesgue spaces", Joint International Meeting of the American, European and Portuguese Mathematical Societies (AMS, EMS and SPM, respectively),  June 10-13, 2015, Porto, Portugal.

  5. "Semi-Plenary talk)’Multisublinear maximal operators in Banach Function Lattices", V Annual International Conference of the Georgian Mathematical Union’’, September 8-12, 2014, (book of Abstracts, P. 47).

  6. "Two-weight criteria for Riesz potentials on cones of radially decreasing functions", Caucasian Mathematics Conference (CMC I), Tbilisi, September 5-6, 2014 (book of abstracts, p. 135).

  7. "Weighted criteria for multilinear fractional integrals", International Congress of Mathematicians  (ICM 2014)", August 13-21, Seoul, Korea.

  8. "Interior estimates and regularity of solutions for elliptic equations in Non-divergence with VMO Coefficients" (Plenary talk), IV International Conference of the Georgian Mathematical Union Dedicated to Academician Victor Kupradze (1903 – 1985) on the occasion of 110-th anniversary of his birthday  and to the Georgian Mathematical union on the occasion  of 90 year from founding, Tbilisi-Batumi, September 9-15, 2013.

  9. "Boundedness and compactness criteria for positive kernel operators in variable exponent Lebesgue spaces", International ISAAC 9-th Congress, 5-9 August, 2013, Krakow, Poland.

  10. "Integral operators in new function spaces: one and two weight problems’, International Conference ‘’Function Spaces X’’, July 9-14, Poznan, Poland.

  11. "One-weighted and trace inequalities criteria for fractional integrals in grand Lebesgue spaces", 8thInternational Conference on 'Function Spaces, Differential Operators, and Nonlinear Analysis' (FSDONA 2011), September 18-24, 2011, Tabarz/Thuringia, Germany.

  12. "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 9-14, 2011.

  13. "Potential and singular operators in grand Lebesgue and Morrey spaces" (Invited Speaker),   5-th World Conference on 21st Century Mathematics, Abdus Salam School of Mathematical Sciences, GC University, Lahore, Pakistan, 9-13 February, 2011.”

  14. "On the Hardy Inequality", Young Researchers  First International Camp, July 25-31, 2010,  Bakuriani, Georgia.

  15. "Weighted estimates for operators of harmonic analysis in non-standard Lebesgue spaces and some applications",  XXXConvegnoNazionale di AnalisiArmonica, Gargnano, 7-11 giugno 2010, Italia.

  16. "One-sided 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 7-13, 2010,Lahore, Pakistan.

  17. "Maximal functions and potentials in Morrey spaces associated with grand Lebesgue spaces", Batumi-Kutaisi, Georgia, 9-12 October, 2009.

  18. "Potentials and singular integrals in Morrey spaces" (Invited Speaker),  4-th World Conference on 21st Century Mathematics, Abdus Salam School of Mathematical Sciences, Lahore, Pakistan, March 4-8, 2009.

  19. "Trace inequalities for fractional maximal and potential operators in Lp(x) spaces", International Workshop  in Variable Exponent Analysis and Related Topics, Tbilisi, Georgia,  September 2-5, 2008. 

  20. "Boundedness of one-sided operators in variable exponent Lebesgue spaces", Workshop and Conference In Function Spaces, Differential Operators and Nonlinear Analysis, Helsinki, Finland, August 22-29, 2008.

  21. (a) "One-sided operators in Lebesgue spaces vith variable exponent";  (b) "Two-weight estimates for gene-ralized 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 3-5, 2007. 

  22. "On the boundedness of one-sided  maximal functions and   singular integrals in Lebesgue spaces with variable exponent", 6-th International ISAAC Congress, Ankara, Turkey, 13-18 August, 2007.

  23. "Two-weight estimates for maximal functions, potentials and singular integrals in variable exponent Lebesgue spaces",  International Workshop in Variable Exponent Analysis, Baku, Azerbaijan, May 14-18, 2007.

  24. "Two-weight estimates for potentials and singular integrals in variable Lebesgue spaces", 3rd International Conference on 21st Century Mathematics, 2007, School of Mathematical Sciences and National Centre for Mathematics, GC University, Lahore, Pakistan,   March 4-7, 2007.

  25. "Two-weight estimates for strong fractional maximal functions and potentials with multiple kernels and application in weighted Strichartz estimates for non-homogenous wave equations" . IV Congress of Georgian Mathematicians, Tbilisi, Georgia, November 14-16, 2005.

  26. "Two-weight 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.

  27. "Stime a due pesi per funzionimassimaliforti e potenziali con nuclei multipli". XXV   ConvegnoNazionale di AnalisiArmonica (Italia), Universita` di Bologna, Dipartimento di Matematica, 6-9 ,aprile 2005,  Organizzatore: Nicola Arcozzi.

  28. "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.

  29. "Fractional integrals on nonhomogeneous spaces ",  7th  International Conference on Harmonic Analysis and Partial Differential Equations, El Escorial, Madrid (Spain) June 21-25, 2004.

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

  31. "On the boundedness and compactness for one-sided 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 1-13, 2003.

  32. "On a trace inequality  for the Riemann-Liouville 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 8-13, 2003.

  33. "On a meassure of non-compactness for the Hardy-Littlewood maximal Functions and Calderon-Zygmund singular integrals", ISAAC  Conference on Complex Analysis, Differential Equations and Related Topics,  Yerevan, Armenia,  Seprember 17-21,   2002.

  34. "On a measure of non-compactness formaximal functions", Congress of Georgian Mathematicians, Tbilisi, Georgia, 11-13 October,  2001.

  35. "On a trace inequality for one-sided 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 23-25,  2001.

  36. "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.

  37. "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.

  38. "Boundedness and compactness weighted criteria for the operators with positive kernels".  European Congress for Mathematics,  Barcelona, July 10-14,  2000.

  39. "Boundedness and compactness weighted criteria for kernel integral operators",  International Symposium in Advanced Course on Function Spaces and Applications, Tbilisi,  Georgia, September 6-10,  1999.

  40. "Two-weight boundedness and compactness criteria for one-sided maximal functions and potentials", The first International Junior Conference in Mathematical Analysis, A. Razmadze Mathematical Institute, Tbilisi, Georgia, April 30- May 1, 1998.

  41. "Weighted Inequalities for the Riemann- Liouvlille and Weyl operators defined on SHT", International Congress of Mathematicians, Berlin, Germany, August 18-27, 1998.

  42. "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.

  43. "Two-weight estimates for singular integrals", Congress of Georgian Mathematicians, Tbilisi, Georgia, September, 1997.

 

14. Scientific and Academic Visits

 

15. Talks in  Seminars:

 

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)      28.09.2009-up 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)       2001-2003:  Tbilisi State University, Georgia,  (Course of Ordinary Differential Equations, Faculty of Differential Equations).

i)        1996-1998: 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; E-mail: kokil@rmi.acnet.ge

2.      Professor David E. Edmunds, Address: School of Mathematics, Cardiff University, Senghennydd Road, Cardiff CF24 4YH, U.K. e-mail:  DavidEEdmunds@aol.com

3.      Professor Stefan Samko, Faculdade de Ciencias e Tecnologia, University do Algarve, Campus de Gambelas, 8005-139 Faro, Portugal, Tel: (351)-289-800-900. ext. 7667; e-mail: ssamko@ualg.pt

4.      Professor Vladimir Georgiev, Address: Department of Mathematics, University of Pisa, 56127, Pisa, Largo Bruno Pontecorvo 5, Italy; Tel. (00)39-050-2213301, E-mail:  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, e-mail: EvansWD@cf.ac.uk

7.      Professor Fulvio Ricci, Scuola Normale Superiore, Piazza dei Cavallieri 7, 56126 Pisa, Italy, Telephone: +39-050-509257, e-mail: 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, e-mail: fiorenza@unina.it

 

18. PhD Students of A. Meskhi:

1.      GhulamMurtaza, Title of the thesis:  “Two-weight criteria for potentials with product kernels on the cone of non-increasing 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 potential-type operators." Abdus Salam School of Mathematical Sciences, Lahore, 2009.

4.      Muhammad Asif, Title of the thesis: “On the boundedness and measure of  non-compactness 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 21-st 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 Non-compactness 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 Non-standard Function Spaces. Vol. I. Variable Exponent Lebesgue and Amalgam Spaces. Birkhäuser, 2015,  pp. 1-586.

5.      V. Kokilashvili, A. Meskhi, S. Samko, and H. Rafeiro, Integral Operators in Non-standard Function Spaces. Vol. II. Variable Exponent Hölder, Morrey-Campanato and Grand spaces. Birkhäuser, 2016,  pp. 587-1009.

 

 

Papers (by the symbol * it is denoted papers published in journals with Impact-Factor)

1.            Two-weight inequalities for singular integrals on Heisenberg groups.  Bull. Acad. Sci. Georgia  153(1996), No. 1, 34-36.

2.            Two- weight inequalities for potentials on homogeneous groups. Bull. Acad. Sci.  Georgia 154(1996), No. 3, 353-355.

3.            Two-weight inequalities for the Hardy operator on the Lorentz spaces defined on homogeneous groups. Proc. A. Razmadze Math. Inst.  112(1997), 138-140 (with V. Kokilashvili).

4.            Two-weight inequalities for singular integrals on the Lorentz spaces defined on homogeneous groups. Proc. A. Razmadze Math. Inst.  112(1997), 143-145 (with V. Kokilashvili).

5.            Two-weight inequalities for potentials on the Lorentz spaces defined on homogeneous groups. Proc. A. Razmadze Math. Inst. 112(1997), 148-150.

6.            Two-weight inequalities for Hardy-type transforms and singular integrals defined on homogeneous type spaces. Proc. A. Razmadze Math. Inst. 114(1997), 119-123 (with V.Kokilashvili).

7.            * Two-weight estimation for singular integrals defined on homogeneous groups.  (Russian)  Doklady Academy Nauk RAN 354(1997) No. 3, 301-303. English transl. in Doklady Mathematics  55(1997), No. 3, 362-364 (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), 57-90 (with V. Kokilashvili).

10.        Two-weight 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 Riemann-Liouville and one-sided maximal operators. Proc. A. Razmadze Math. Inst. 117(1998),126-128.

13.        Weighted inequalities for Riemann-Liouville transform, Proc. A. Razmadze Math. Inst. 117(1998), 151-153.

14.        * Solution of some weight problems for the Riemann-Liouville and Weyl operators. Georgian Math. J.  5(1998), No. 6, 265-274.

15.        Two-weight inequalities for a discrete Hilbert transform.  Proc. A. Razmadze Math. Inst. 116(1998), 107-122. (with I. Gabisonija).

16.        Two-weight inequalities for a discrete Hardy operators and Hilbert transform. Bull. Acad. Sci. Georgia 158(1998), No. 2, 191-193 (with I. Gabisonija).

17.        Boundedness and compactness of Hardy-type operators in Banach function spaces. Proc. A. Razmadze Math. Inst.  117(1998), 7-30 (with D. E. Edmunds and V. Kokilashvili).

18.        * Two-weight 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 Riemann-Liouville  operator.  Proc. A. Razmadze Math. Inst. 121(1999), 161-162.

20.        On the boundedness and compactness of ball fractional integral operators.  Fract. Calc.  Appl. Anal. 3 (2000), No. 1, 13-30.

21.        On the measure of non-compactness and singular numbers for the Volterra integral operators. Proc. A. Razmadze Math. Inst.  123(2000), 162-165.

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, 273-296, 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, 28-31, 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.), 247-253, Kluwer Academic Publishers, Dordrecht (The Netherlands), 2001 (with V. Kokilashvili).

25.        *  Two-weight estimates for singular integrals defined on spaces of homogeneous type.  Canadian J. Math.  52(2000), No. 3, 468-502 (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), 59-78 (with V. Kokilashvili).

27.        Criteria of the boundedness and compactness for generalized one-sided potentials.  Real Anal. Exchange 26(2000/2001), No. 1, 217- 236.

28.        * Criteria for the boundedness and compactness of operators with power-logarithmic kernels.  Analysis Math.  27(2001), No. 2, 173- 185 (with V. Kokilashvili).

29.        On the boundedness and compactness criteria for the Riemann-Liouville type discrete operator. Proc. A. Razmadze Math. Inst.  126(2001), 117-119.

30.        * Criteria for the boundedness and compactness of integral transforms with positive kernels, Proc. Edinburgh Math. Soc.  44(2001), 267-284.

31.        * Weight inequalities for singular integrals defined on spaces of homogeneous and nonhomogeneous type. Georgian Math. J.  8(2001), No. 1, 33-59 (with D. E. Edmunds and V. Kokilahsvili).

32.        * Asymptotic behavior of singular and entropy numbers for some Riemann-Liouville type operators. Georgian Math. J. 8(2001), No. 2, 323- 332.

33.        * On a trace inequality for one-sided potentials and applications to the solvability of nonlinear integral equations. Georgian Math. J. 8(2001), No. 3. 521-536 (with V. Kokilashvili).

34.        Fractional integrals on measure spaces,  Fract. Calc. Appl. Anal. 4(2001), No.1. 1-24 ( With V. Kokilashvili).

35.        *  On the singular numbers for some integral operators.  Revista Mat. Compl. 14(2001), No. 2, 379-393.

36.        Boundedness and compactness criteria for the generalized truncated potentials (Russian), Proc. Steklov Math. Inst. RAN 232(2001), 164-178. Engl. Transl. In: Proc. Steklov Inst. Math. 232(2001) (with V. Kokilashvili).

37.        On a measure of non-compactness for the Riesz transforms. Proc. A. Razmadze Math. Inst. 129 (2002), 156-157.

38.        *  On Fourier multipliers in weighted Triebel-Lizorkin spaces, J. Inequal. Appl. 7(2002), No. 4, 555-591 (with. D.E.Edmunds and V. Kokilashvili) .

39.        * Potential-type operators in $L^{p(x)}$ spaces,  Z. Anal. Anwend.   21(2002), No. 3, 681-690 (with D.E. Edmunds).

40.        Weight inequalities for one-sided potentials for critical weights.  Fract.  Calc.  Appl. Anal.  5(2002), No.3, 255-265 (with V. Kokilashvili).

41.        * On a measure of non-compactness for maximal operators. Math. Nachr.  254-255 (2003), 97-106 (with D.E. Edmunds).

42.        * On a measure of non-compactness for singular integrals.  J. Funct. Spaces  Appl. 1(2003), No.1, 35-43.

43.        On the inversion and characterization of the Riesz potentials in the weighted Lebesgue spaces. Mem. Differential Equation Math. Phys. 29(2003), 31-45 (with V. Kokilashvili and S. Samko).

44.        On a trace inequality for one-sided 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, 55-69 (with D. E. Edmunds and V. Kokilashvili).

46.        On two-weight inequalities for multiple Hardy-type  operators. Proc. A. Razmadze Math. Inst.  136(2004), 149-153.

47.        On two-weight estimates for strong fractional maximal functions and potentials with multiple kernels.  Proc. A. Razmadze Math. Inst. 137(2005), 135-140  (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, 27-44 (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), 132-136  (with V. Kokilashvili and Ts. Tsanava).

50.        On a weighted Strichartz estimate for inhomogeneous wave equations. Proc. A. Razmadze Math. Inst.  139(2005), 96-99 (with V. Georgiev).

51.        *  On one-sided potentials with multiple kernels. Integral Transf. Spec. Funct. 16 (2005), No. 8, 669-683.(with V. Kokilashvili).

52.        *  On some two-weight inequalities for fractional integrals on nonhomogeneous spaces, Z. Anal. Angewend. 24(2005), No. 4, 871-885 (with V. Kokilashvili).

53.        *  A note on two-weight inequalities for multiple Hardy-type operators, J. Funct. Spaces  Appl.  3(2005), 223-237.

54.        Two-weighted 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), 119-140 (with V. Kokilashvili).

55.        Two-weight 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), 123-128 (with D. Edmunds and V. Kokilashvili).

56.        *  On a measure of non-compactness for some classical operators. Acta Math. Sinica (Eng. Series) 22(6)(2006), 1847-1862 (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), 121-125 (with U. Ashraf and M. Asif).

58.        On one-sided operators in variable exponent Lebesgue spaces. Proc. A. Razmadze Math. Inst. 144(2007), 126-131 (with D. E. Edmunds and V. Kokilashvili). 

59.        On two-weight criteria for maximal function in  $L^{p(x)}$ spaces defined on an interval.  Proc. A. Razmadze Math. Inst. 145(2007), 100-102  (with V. Kokilashvili).

60.        Two-weight 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 3-5, 2007. Published in “Evrazii’skii’ Matematicheskii’ Zhurnal” No. 2, 2007, 31-46  (with V. Kokilashvili).

61.        * Two-weight estimates for singular and strongly singular integral operators. Acta Math. Hungar. 116 (2007), No. 1-2, 1-25 (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, 609-628 (with V. Kokilashvili).

63.        On the maximal and Fourier operators in weighted Lebesgue spaces with variable exponent, Proc. A. Razmadze Math. Inst. 146 (2008), 120-123 (with V. Kokilashvili).

64.        Maximal and potential operators in variable Morrey spaces defined on non-homogeneous spaces. Bull. Georgian National Acad. Sci.  2(2008), No. 3, 18-21 (with V. Kokilashvili).

65.        One and two weight estimates for one-sided 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,  208-223 (with M. Asif).

67.        Boundedness of maximal and singular operators in Morrey spaces with variable exponent, Armenian J. Math. 1(2008), No.1, 18-28  (with V. Kokilashvili).

68.        * Weighted estimates of a measure of non-compactness for maximal and potential operators. J. Inequal. Appl. 2008, Art.  ID 697407, 19 pages  (with M. Asif).

69.        *  One-sided operators in $L^{p(x)}$ spaces. Math. Nachr. 281(2008), No. 11, 1525–1548  (with D. E.   Edmunds and V. Kokilashvili).

70.        * Two-weight estimates in  $L^{p(\cdot)}$ spaces with applications to Fourier series. Houston Journal of Mathematics 35(2009) , No. 2, 665-689 (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/s11117-008-2217-8, 497-518  (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), 139-143.

73.        Two-weight estimates for maximal, potential and singular operators in $L^{p(x)}$  spaces. Proc. A. Razmadze Math. Inst. 149(2009), 122-125 (with V. Kokilashvili).

74.        Two-weight criteria for one-sided strong fractional maximal functions. Proc. A. Razmadze Math. Inst. 149(2009), 118-121. (with V. Kokilashvili).

75.        * Boundedness criteria for maximal functions and potentials on the half-space in weighted  Lebesgue spaces with variable exponents. Integr. Transf. Spec. Func. 20(2009), No. 11, 805-819 (with M. Asif  and  V. Kokilashvili).

76.        * Two-weight 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), 227-239 (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, 547-551  (with V. Kokilashvili).

79.        * Maximal functions and potentials in variable exponent Morrey spaces with non-doubling measure. Complex Variables and Elliptic Equations 55 (2010), No. 8,  923-936  (with V. Kokilashvili).

80.        Two-weight criteria for potentials with product kernels on cones of decreasing functions. Proc. A. Razmadze Math. Inst. 152(2010), 144-153 (with G. Murtaza and M. Sarwar).

81.        Weight characterization of the trace inequality for the generalized Riemann-Liouville transform in $L^{p(x)}$ spaces. Math. Ineq. Appl. 13(2010), No.1, 63-81 (with U. Ashraf and V. Kokilashvili).

82.        One and two weight estimates for one-sided  operators in $L^{p(\cdot)}$ spaces. Eurasian Math. J. 1(2010), No. 1, 73-110  (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 one-sided 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.        Two-weight  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, 622-636. 

88.        * Potential operators on cones of non-increasing functions. J. Funct. Spaces Appl. 2012, Article ID 474681, 26 pages, 2012. doi:10.1155/2012/474681 (with G. Murtaza).

89.        Two-weighted 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. 105-124  (with V. Kokilashvili).

90.        Potentials with product kernels in grand Lebesgue spaces. Proc. A. Razmadze Math. Inst. 159 (2012), 158-161 (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/gmj-2012-0020 (with  M. A. Zaighum).

92.        * Trace inequalities for integral operators with fractional order in grand Lebesgue spaces, Studia Math. 210 (2012), 159-176, DOI: 10.4064/sm210-2-4 (with V. Kokilashvili).

93.        Weight characterization of the boundedness for the Riemann-Liouville 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, 43-64  (with  V. Kokilashvili  and H. Rafeoro).

95.        * Potentials with product kernels in grand Lebesgue spaces: One-weight criteria. Lithuanian Math. J. 53 (2013), No.1, 27-39' (with V. Kokilashvili).

96.        * Positive kernel operators in $L^{p(x)}$ spaces. Positivity 17 (2013), No. 4, 1123-1140; DOI 10.1007/s11117-013-0225-9-9 (with V. Kokilashvili and M. A. Zaighum).

97.        * Weighted kernel operators in variable exponent amalgam spaces, J. Ineq. Appl. 2013, 2013:173, doi:10.1186/1029-242X-2013-173, pp. 1-28,  (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, 159-178 (with V. Kokilashvili and H. Rafeiro).

99.        * Two-weight norm estimates for maximal and Calderón-Zygmund operators in variable exponent Lebesgue spaces. Georgian Math. J. 20 (2013), No. 3, 547-572 (with V. Kokilashvili and M. Sarwar).

100.    * Kernel operators on the upper half-space:  boundedness and compactness criteria. Turkish J. Math. 38 (2014), No. 1, 119-135 (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, 123-152 (with M. A. Zaighum).

102.    * On the boundedness of the multilinear fractional integral operators. Nonlinear Analysis, Theory, Methods and Applications 94 (2014), 142-147 (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, 1169-1184  (with V. Kokilashvili and H. Rafeiro).

104.    * Grand Bochner-Lebesgue space and its associate space. Journal of Functional Analysis 266 (2014), No. 4, 2125-2136 (with V. Kokilashvili and H. Rafeiro).

105.    * Two-weight norm estimates for sublinear integral operators in variable exponent Lebesgue spaces, Studia Sci. Math. Hungarica 51 (2014), No. 3, 384-406  (with V. Kokilashvili).

106.    One-weight weak-type estimates for fractional and singular integrals in grand Lebesgue spaces. Banach Center Publications 102 (2014), 131-142 (with V. Kokilashvili).

107.    Some fundamental inequalities for trigonometric polynomials in imbeddings of grand Besov spaces. Proc. A. Razmadze Math. Inst. 165 (2014), 105-116 (with V. Kokilashvili).

108.    * Maximal and Calderón-Zygmund operators in grand variable exponent Lebesgue spaces. Georgian Math. J. 21 (2014), No. 4, 447-461 (with V. Kokilashvili).

109.    * The multisublinear maximal type operators in Banach function lattices, J. Math. Anal. Appl. 421 (2015), No. 1, 656-668 (with V. Kokilashvili and M. Mastylo).

110.    * Fractional integral operators between Banach function lattices, Nonlinear Analysis, Theory, Methods and Applications 117 (2015) 148-158 (with V. Kokilashvili and M. Mastylo).

111.    * Two-weight norm estimates for multilinear fractional integrals in classical Lebesgue spaces, Fractional Calculus Applied Analysis 18 (2015), No. 5, 1146-1163 (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/jmi-10-50 (with M. A. Zaighum).

114.    * Sharp weighted bounds for one-sided operators, Georgian Mathematical Journal (accepted) (with V. Kokilashvili and   M. A.  Zaighum).

115.   * Weighted extrapolation in Iwaniec-Sbordone spaces. Applications to integral operators and theory of approximation. (Russian) Trudy MIAN  293 (2016),  167–192 (with V. Kokilashvili).

116.   * Interpolation on variable Morrey spaces defined on quasi-metric measure spaces, J. Functional Analysis 270 (2016), No. 10,  3946-3961 (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).