# 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.

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:

b) 1990-1995 - Student of  the  Technical University of Georgia.

8.    Scientific degrees:

a)  2017: Scholar of the Georgian National Academy of Sciences;

b)  2009: Professor;

c)  2001: Doctor of Sciences of Phys.-Math.: "Boundedness and compactness criteria  for potential- type operators". A. Razmadze Mathematical Institute (Scientific Consultant  Prof. V.  Kokilashvili).

d) 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).

e) 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:

b)

c)

d)     2000: Euler Premium for young scientists established by the German Mathematical Association

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.

d)

j)

6.

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

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).

h)    Member of the Editorial Board of  open access  international journal  ‘’ Journal of Advances in Mathematical Analysis and Applications’’  (JAMAA).

i)    Member of Editorial Board of the Impact-Factor Journal ‘’Journal  Nonlinear Sciences and Applications’’ (J. Nonlinear Sci. Appl.).

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).

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.

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

34.        *

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

37.

42.

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).

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.  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 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).

118.   * Multilinear integral operators in weighted grand Lebesgue spaces, Frac. Calc. Appl. Anal. 19 (2016), 691-724. (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., DOI: 10.1515/gmj-2016-0041  (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, 558-560.

122.   The Riemann–Hilbert problem in the class of Cauchy type integrals with densities of grand Lebesgue spaces, Trans. A. Razmadze Math. Inst. 170 (2016), No. 2, 208-211 (with V. Kokilashvili and V. Paatashvili).

123.   Generalized singular integral on Carleson curves in weighted grand Lebesgue spaces, Trans. A. Razmadze Math. Inst. 170 (2016), No. 2, 212-214 (with V. Kokilashvili and V. Paatashvili).

124.   * Complex interpolation on variables exponent Campanato spaces of order k, Complex variable and Elliptic Equations (accepted) (with H. Rafeiro and M. A. Zaighum).