a) First name: ALEXANDER
b) Family name: MESKHI
c) Date of birth: May 2, 1972.
d) Place of birth:
e) Citizenship: Citizen of
f) Marital status: Married.
g) Children: Two sons
2. Positions:
a) 22.06.2022 - up to now: Head of the Department of Mathematical Analysis at A. Razmadze Mathematical Institute of I. Javakhishvili Tbilisi State University.
b) April 14 2020 - up to now: Professor of Kutaisi International University.
c) 12.02.2018 - up to now: Chief Researcher of A. Razmadze Mathematical Institute of I. Javakhishvili Tbilisi State University
d) 11.05.2000 - 11.02.2018: Senior Researcher at A.Razmadze Mathematical Institute, Georgia
e) 28.09.2009 - 31.08.2020: Full
Professor of the
Technical University of Georgia (Department of Mathematics).
f) 01.2006 - up to now: Foreign Professor of Abdus Salam School of Mathematical Sciences, GC University,
g) 01.05.2003 - 01.05.2005: Postdoc
position at Scuola Normale Superiore of
e) 02.10.1998 - 11.05.2000: Researcher at A. Razmadze Mathematical Institute, Georgia.
3. Services;
Editorship:
a) 2022- President of the Georgian Mathematical Union;
b) 2016- Editor in Chief of ''Transactions of A. Razmadze Mathematical
Institute'';
c) 2021, 2022: Chair of the Organizing Committee of the Annual International
Conference of GMU.
4. Mailing Addresses:
(a) A. Razmadze Mathematical Institute
of I. Javakhishvili Tbilisi State University, 2, Merab Aleksidze II Lane,
Tbilisi 0193, Georgia;
(b) Youth Avenue, 5th Lane, K Building, Kutaisi, 4600 Georgia
5. e-mail: alexander.meskhi@tsu.ge; alexander.meskhi@kiu.edu.ge
6. Tel. :(+995) 93 57 38 95.
7. Languages: Georgian (Mother), Russian, English, Italian.
8.
Education:
a) 1995-1998 - Post-graduate Student of A. Razmadze Mathematical Institute
b) 1990-1995 - Student of
the
9. 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".
10. Main Research Field: Harmonic Analysis and Applications in Partial Differential Equations.
11. 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.
12. 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)
o) 25.08.2017 – 31.08.2017: Study the boundedness of sublinear operators in grand Morrey spaces in the framework of doubling metric spaces, Pontificia Universidad Javeriana, Convocatoria n° 015 de 2017 - movilidad de profesores para desarrollar investigación con instituciones extranjeras, Project Number 7905.
p) 30.06.2016-06.07.2016: Shota Rustaveli National Science Foundation Grant, Name of the Project ’’ The 11th AIMS Conference on Dynamical Systems, Differential Equations and Applications’’, Contract No. 03/63.
q) 13.08.2014-21.08.2014: Shota Rustaveli National Science Foundation Grant, Name of the Project: ‘’International Congress of Mathematicians (ICM 2014)’’, Project No. 2014_tr_563.
r) 2019-2021: Rustaveli National Science Foundation Grant ‘’ Integral Operators in Non-standard Function Spaces; New Aspects of Fourier Analysis and Wavelet Theory’’, Project No. DI 18-118.
s) 01.03.2019-01.03.2022: Rustaveli National Science Foundation Grant ‘’New approaches in modern analysis on metric spaces, multidimensional and Applied Harmonic Analysis. Applications to PDEs’’, Project No. FR-18-2499.
t) 27.05.2019-31.05.2019: ERASMUS+ ICM Project (Ref. 2017-1-PT01-KA107-035493), University of Aveiro, Portugal. Short Course of Lectures ’’Integral operators in grand Lebesgue spaces’’.
u) 31.01.2023-31.01-2024: Grant of BSU, “Problems of the multilinear extrapolation and approximation theory in function spaces of Grand and Morrey type”, Resolution of the Academic Council of BSU ¹06-01/04.
13. 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.
d)
2000:
Euler Premium for young scientists established by the
German Mathematical Association (Germany).
14. Participation in Conferences, Congresses, Schools, etc:
"Extrapolation in mixed-normed function spaces and applications", KIU Annual Conference, Math and Computer Science, July 11-13, 2023.
"Boundedness criteria and sharp estimates for multilinear fractional integral operators", International Seminar, Yildiz Technical University International Mathematical Analysis Society, November 23, 2022.
"Multilinear fractional integrals: boundedness criteria and sharp estimates" (Invited Speaker), Recent Advances in Analysis and Applications, Al Ain, UAEU, October 19-20, 2022.
"Operators of Harmonic Analysis in Grand Variable Exponent Morrey Spaces", International Conference on “Function Spaces and Applications” (FSA-2020), Apolda, Germany, October 1 - 7, 2022.
"Weighted extrapolation in grand Morrey spaces beyond the Muckenhoupt range", XII Annual International Conference of the Georgian Mathematical Union, Batumi, August 29 – September 03, 2022.
"Sharp Olsen's and trace inequalities for multilinear fractional integrals", KIU Annual Conference, Math and Computer Sciences, Mini-symposium Analysis and Related Topics, July 12-14, 2022, Kutaisi International University, Georgia.
"Fractional integrals with measure in grand Lebesgue and Morrey spaces", 8th European Congress of Mathematics, Portorož, Slovenia, 20-26 June, 2021.
"On the essential norm for multilinear operators", 13th ISAAC Congress, August 2–August 6, 2021, Ghent, Belgium.
"Maximal and singular integral operators in weighted Lebesgue spaces of Banach-valued functions", Modern Movement of Science: abstracts of the 12th International Scientific and Practical Internet Conference, April 1-2, 2021. – Dnipro, Ukraine.
"Weighted extrapolation and boundedness in generalized grand Morrey spaces, and applications to partial differential equations", XI Annual International Conference of the Georgian Mathematical Union, August 23-28, 2021, Batumi, Georgia.
"Trace Inequalities for Fractional Integrals in Central Morrey Spaces" (with G. Imerlishvili), Book of Abstracts, of XI International Conference of the Georgian Mathematical Union, August 23-28, 2021, Batumi.
"On a weighted inequality for fractional integrals" (with G. Imerlishvili), 8th European Congress of Mathematics, Portorož, Slovenia, 20-26 June, 2021.
"Weighted inequalities for one-sided multilinear integral operators", 3rd International Conference on Mathematical and Related Sciences: Current Trends and Developments (ICMRS 2020), 20-22 November 2020, Antalya, Turkey (Online Conference) http://www.ic-mrs.org/.
"Weighted multilinear Rellich and Hardy inequalities" (Online conference), 3rd International Conference on Mathematical and Related Sciences: Current Trends and Developments (ICMRS 2020), 20-22 November 2020, Antalya, Turkey(Online conference) http://www.ic-mrs.org/
"The weight estimates for one-sided multilinear fractional integrals" (with G. Imerlishvili), XXXIV International Enlarged Sessions of the Seminar of Ilia Vekua Institute of Applied Mathematics (VIAM) of Ivane Javakhisvili Tbilisi State University (TSU), September 16-19, 2020.
"Boundedness criteria for maximal and singular integral operators in weighted variable exponent Lebesgue spaces", XXXIV International Enlarged Sessions of the Seminar of Ilia Vekua Institute of Applied Mathematics (VIAM) of Ivane Javakhisvili Tbilisi State University (TSU), September 16-19, 2020.
"Measure of non-compactness for multisublinear maximal functions and multilinear singular integrals", X Annual International Meeting of the Georgian Mechanical Union, September 26-28, 2019, Telavi, Georgia.
"Maximal and Calderon-Zygmund operators in extrapolation Banach function lattices and applications", 12-th ISAAC Congress, July 29- August 2, 2019, Aveiro, Portugal.
"Singular integrals in weighted grand variable exponent Lebesgue spaces", 12-th ISAAC Congress, July 29- August 2, 2019, Aveiro, Portugal.
"On the Rellich Inequality in Variable Exponent Lebesgue Spaces", International Congress of Mathematicians (ICM2018), August 1-9, Rio de Janeiro, Brazil.
"Weighted extrapolation in grand Lebesgue spaces and some applications", New Persectives in Function Spaces and Applications’’ (NPFSA 2017), September 17-23, 2017 , Bedlewo, Poland.
"Integral Operators of Harmonic Analysis in Grand Variable Exponent Lebesgue Spaces" (Invited Speaker), Banach Spaces and Operator Theory with Applications, July 3-7, 2017, Adam Mickiewicz University, Poznan, Poland, (Book of Abstracts, p. 29);
"Sublinear perators in weighted grand Morrey spaces", The 11th AIMS Conference on Dynamical Systems, Differential Equations and Applications, July 1-5, 2016, Orlando, Florida, USA (Book of Abstracts, p. 179).
"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.
"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.
"Fractional integral operators between Banach function lattices" (Invited Speaker), International Workshop on Operator Theory and Applications (IWOTA 2015), July 6-10, Tbilisi, Georgia.
"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.
"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).
"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).
"Weighted
criteria for multilinear fractional integrals",
International Congress of Mathematicians (ICM
2014)", August 13-21, Seoul, Korea.
"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.
"Boundedness
and compactness criteria for positive kernel operators in
variable exponent Lebesgue spaces", International ISAAC 9-th Congress,
5-9 August, 2013, Krakow, Poland.
15.
Scientific and Academic Visits
2019 (May 25-June 02) University of Aveiro, Portugal.
2018 (November 4-10) Beijing Normal University, China.
2018 (September 10-15) Adam Mickiewicz University of Poznan, Poland.
2018 (28 May- 8 June) Adam Mickiewicz University of Poznan, Poland.
2017 (August 23-28) Pontificia Universidad Javeriana, Bogota, Columbia
2016 (January 25- February 25), San Diego State University, USA.
2014 (October 7-16) Adam Mickiewicz University of Poznan, Poland.
2013 (June 23-July 2) Adam Mickiewicz University of Poznan, Poland.
2005
(June 1- September 1), Department of Mathematics, University of Pisa, Italy.
2004
(November), University of Naples, department of mathematics (Italy).
1999
(March), University of Sussex, Cardiff University (UK);
1998 (June 1- 7), Mathematical Institute of the Czech Republic.
07.02.2023. "Boundedness criteria for multilinear fractional integral operators” , Tbilisi Analysis & PDE Seminar.
23.11.2022. "Boundedness criteria and sharp estimates for multilinear fractional integral operators“, International Mathematical Analysis Society, Yildiz Technical University.
09.11.2018. "Multilinear fractional integrals in weighted function spaces", Beijing Normal University, China, School of Mathematical Sciences (Head of the Seminar, Professor Qingying Xue).
29.05.2018. "Weighted Extrapolation in Grand Lebesgue Spaces defined on Product Sets", Adam Mickiewicz University of Poznan, Faculty of Mathematics and Computer Sciences'' ( Head of the Seminar, Professor M. Mastylo).
j)
Experience in Working with PhD Students.
18.
PhD Students of A. Meskhi:
5. M. A. Zaighum, Title of the thesis: “Kernel operators in some new function spaces”, Abdus Salam School of Mathematical Sciences, Lahore, 2014.
6. Giorgi Imerlishvili, Title of the thesis "Weighted estimates for multilinear fractional integrals,", Georgian Technical University, 2023.
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);
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.);
j) Member of Editorial Board of ''Georgian Mathematical Journal'' (De Gruyter);
k) Member of Editorial Board of ''Journal of Function Spaces and Applications'' (Hindawi).
List
of Publications of A. Meskhi
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)
20.
*
On the boundedness and compactness of ball fractional integral operators.
Fract. Calc. Appl. Anal. 3 (2000), No. 1, 13-30.
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).
40.
*
Weight inequalities for one-sided potentials for critical weights. Fract.
Calc. Appl. Anal. 5(2002), No.3, 255-265 (with V. Kokilashvili).
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).
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).
93. Weight characterization of the boundedness for the Riemann-Liouville discrete transform. J. Prime Res. Math. 9 (2013), 34-50 (with G. Murtaza).
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. * 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).
115. * 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).
116. Sharp weighted bounds for multiple integral operators, Trans. A. Razmadze Math. Inst. 170 (2016), 75–90 (with V. Kokilashvili and M. A. Zaighum).
117. * Multilinear integral operators in weighted grand Lebesgue spaces, Frac. Calc. Appl. Anal. 19 (2016), 691-724. (with V. Kokilashvili and M. Mastylo).
118. 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).
119. * 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).
120. * 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.
121. 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).
122. 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).
123. * Sharp weighted bounds for one-sided operators, Georgian Math. J. 24 (2017), No. 2, 227-240 (with V. Kokilashvili and M. A. Zaighum).
124. * Complex interpolation on variable exponent Campanato spaces of order $k$, Complex Variable and Elliptic Equations 62 (2017), No. 6, 795-813 (with H. Rafeiro and M. A. Zaighum).
125. * Hardy-Littlewood maximal operator in weighted grand variable exponent Lebesgue space, Mediterranean J. Math. 14 (2017), No. 3, Art 118, 20 pp. (DOI 10.1007/s00009-017-0921-y) (with A. Fiorenza and V. Kokilashvili).
126. * Central Calderon-Zygmund operators on Herz type Hardy spaces of variable smoothness and integrability. Ann. Funct. Anal. 9 (2018), No. 3, 310-321 (with H. Rafeiro and M. A. Zaighum).
127. The Boundedness of sublinear operators in weighted Morrey spaces defined on spaces of homogeneous type. In: Jain P., Schmeisser HJ. (eds.), Function Spaces and Inequalities. Springer Proceedings in Mathematics & Statistics, vol. 206, pp 193-211, Springer, Singapore, 2017 (with V. Kokilashvili).
128. * On the boundedness of Marcinkiewicz integrals on continual variable exponent Herz spaces. Georgian Math. J. (with H. Rafeiro and M. A. Zaighum), Published online, DOI: https://doi.org/10.1515/gmj-2017-0050.
129. * Interpolation of an analytic family of operators on variable exponent Morrey spaces. Hiroshima Math. J. 48 (2018), no. 3, 335-346. (with H. Rafeiro and M. A. Zaighum).
130. * One-sided Operators in Grand Variable Exponent Lebesgue Spaces, Zeitschrift fur Analysis und ihre Anwendungen 37 (2018), No. 3, 251-375 (with V. Kokilashvili).
131. * On the Rellich inequality in $L^{p(\cdot)}(a,b)$. Georgian Math. J. 25 (2018), no. 2, 207-216 (with D. Edmunds).
132. * Density, duality and preduality in grand variable exponent Lebesgue and Morrey spaces. Medit. Mediterranean J. Math. (2018) 15: 100. DOI: https://doi.org/10.1007/s00009-018-1145-5 (with Y. Sawano).
133. * Extrapolation in grand Lebesgue spaces with weights, Math. Notes 104 (2018), No. 4, 51–62, DOI: 10.1134/S0001434618090055 (with V. Kokilashvili).
134. * Extrapolation results in grand Lebesgue spaces defined on product sets, Positivity 22(4) (2018), 1143-1163, DOI: https://doi.org/10.1007/s11117-018-0564-7 (with V. Kokilashvili).
135. * Sharp weighted bounds for fractional integrals via the two-weight theory, Banach J. Math. Anal. 12 (2018), No. 3, 673-692, DOI:10.1215/17358787-2017-0063 (with V. Kokilashvili and M. A. Zaighum).
136. * Two-weighted Hardy operator in $L^{p(x)}$ spaces and applications, Studia Math. 249 (2019), 143-162, DOI: 10.4064/sm180204-20-8 (with D. E. Edmunds).
137. * Weighted Extrapolation in Grand Morrey Spaces and Applications to Partial Differential Equations, Rendiconti Lincei Matematica e Applicazioni 30 (2019), 67–92; DOI 10.4171/RLM/836 (with V. Kokilashvili and M. A. Ragusa).
138. * Sobolev-type Inequalities for Potentials in Grand Variable Exponent Lebesgue Spaces, Math. Nachr. 292 (2019), No.10, 2174-2188, DOI: 10.1002/mana.201800239 (with D. E. Edmunds and V. Kokilashvili).
139. * On the Boundedness of Multilinear Fractional Integral Operators, J. Geom. Anal. 30 (2020), no. 1, 667-679, https://doi.org/10.1007/s12220-019-00159-6, 2019 (with V. Kokilashvili and M. Mastylo).
140. * Commutators of Sublinear Operators in Grand Morrey Spaces. Studia Sci. Math. Hungarica 56 (2019), 211–232, no. 2, 211-232, DOI: 10.1556/012.2019.56.2.1425 (with V. Kokilashvili and H. Rafeiro).
141. * The measure of noncompactness of multilinear operators. Nonlinear Analysis 188 (2019), 70–79; https://doi.org/10.1016/j.na.2019.05.011 (with V. Kokilashvili and M. Mastylo).
142. * Compactness criteria for fractional integral operators. Fract. Calc. Appl. Anal. 22 (2019), no. 5, 1269-1283 (with V. Kokilashvili and M. Mastylo).
143. * Extrapolation in Weighted Classical and Grand Lorentz Spaces. Application to the Boundedness of Integral operators, Banach Journal of Mathematical Analysis 4 (2020), 1111-1142, https://doi.org/10.1007/s43037-020-00054-1 (with V. Kokilashvili).
144. Essential Norm Estimates for Multilinear Singular and Fractional Integrals, Commenatationes Mathematicae 59 (2019), No. 1-2, 81–93.
145. Multilinear Fefferman-Stein type inequality and its generalizations, Trans. A. Razmadze Math. Inst. 174 (2020), No. 1, 83-92 (with G. Imerlishvili and Q. Xue).
146. *A note on the trace inequality for Riesz potentials, Georgian Math. J. (accepted), DOI: 10.1515/gmj-2020-2077 (with G. Imerlishvili)
147. * Singular integral operators in some variable exponent Lebesgue spaces, Georgian Math. J., https://doi.org/10.1515/gmj-2020-2065, Published online: 16 Jul 2020 (with V. Kokilashvili and M. Mastylo).
148. *Weighted Sobolev inequality in grand mixed norm Lebesgue spaces, Positivity 25 (2021), 273-288, DOI: 10.1007/s11117-020-00764-8 (with V. Kokilashvili).
149. *Boundedness of integral operators in generalized weighted grand Lebesgue spaces with non-doubling measures, Mediterranean J. Math. 18 (2021), 50, https://doi.org/10.1007/s00009-020-01694-1 (with V. Kokilashvili).
150. *On integral operators in weighted grand Lebesgue spaces of Banach-valued functions, Mathematical Methods in the Applied Sciences, DOI: 10.22541/au.158679979.93141945. (with V. Kokilashvili).
151. *On the boundedness of integral operators in weighted grand Morrey spaces (in Russian), Proc. Steklov. Math. Inst., https://doi.org/10.4213/tm4134 (with V. Kokilashvili).
152. * Calderon--Zygmund singular operators in extrapolation spaces, Journal of Functional Analysis 279 (2020), Issue 10, 108735, DOI: https://doi.org/10.1016/j.jfa.2020.108735 (with V. Kokilashvili and M. Mastylo).
153. Maximal and Calder\'on--Zygmund operators in weighted grand variable exponent Lebesgue spaces, Trans. A. Razmadze Math. Inst. 173 (2019), no. 2, 127-131 (with V. Kokilashvili).
154. Weighted multilinear Hardy and Rellich inequalities, Trans. A. Razmadze Math. Inst. 174 (2020), no. 3, 395-398.
155. Weighted norm estimates for one-sided multilinear integral operators, Trans. A. Razmadze Math. Inst. 174 (2020), No. 3, 399-403 (with G. Imerlishvili).
156. *Trace inequalities for fractional integrals in mixed norm grand Lebesgue spaces, Fract. Calc. Appl. Anal. 23 (2020), no. 5, 1452-1471; DOI: https://doi.org/10.1515/fca-2020-0072 (with V. Kokilashvili).
157. *A Multilinear Rellich Inequality, Mathematical Inequalities and Applications (MIA) 24 (2021), 265-274, DOI: doi:10.7153/mia-2021-24-19 (with D. E. Edmunds).
158. * Fractional integrals with measure in grand Lebesgue and Morrey spaces, Int. Transf. Spec. Funct. 32 (2021), 9, DOI:10.1080/10652469.2020.1833003 (with V. Kokilashvili).
159. *Embeddings in grand variable exponent function spaces, Results Math. 76 (2021), no. 3, Paper No. 137, 27 pp. DOI 10.1007/s00025-021-01450-1 (with D. E. Edmunds and V. Kokilashvili).
160. Weighted extrapolation in mixed norm function spaces, Trans. A. Razmadze Math. Inst. 175 (2021), no. 2, 287-291 (with V. Kokilashvili).
161. Sharp Olsen's inequality for multilinear Riesz potentials, Trans. A. Razmadze Math. Inst. 175 (2021), no. 3, 433-443 (with L. Grafakos).
162. *Maximal and singular integral operators in weighted Grand variable exponent Lebesgue spaces, Ann. Funct. Anal. 12 (2021), no. 3, Paper No. 48, 29 pp. DOI 10.1007/s43034-021-00135-8 (with V. Kokilashvili).
163. *Extrapolation and boundedness in grand variable exponent Lebesgue spaces without assuming the log-Holder condition and application. J. Fourier Anal. Appl. 28 (2022), no. 2, Paper No. 28, 26 pp. DOI: 10.1007/s00041-022-09919-5 (with V. Kokilashvili).
164. On some extrapolation in generalized grand Morrey spaces and applications to partial differential equations, Trans. Razmadze. Math. Inst. 176 (2022), no. 3, 435-441 (with E. Gordadze and M. A. Ragusa).
165. Weighted extrapolation in grand Morrey spaces beyond the Muckenhoupt range, Trans. A. Razmadze Math. Inst. 176 (2022), no. 2, 285-289.
166. Compactness of fractional type integral operators on spaces of homogeneous type, J. Math. Sci. 268 (2022), no. 3, 368-375; DOI 10.1007/s10958-022-06202-2 (with V. Kokilashvili).
167. *Weighted inequalities for one-sided multilinear fractional integrals. Positivity 27 (2023), no. 1, Paper No. 1, 21 pp. 10.1007/s11117-022-00954-6 (with G. Imerlishvili)
168. *Boundedness of operators of harmonic analysis in grand variable exponent Morrey spaces. Mediterr. J. Math. 20 (2023), no. 2, Paper No. 71. https://doi.org/10.1007/s00009-023-02267-8 (with V. Kokilashvili).
169. *Rubio de Francia's weighted extrapolation in mixed norm spaces and applications. Math. Nachr., DOI: 10.1002/mana.202100244 (with V. Kokilashvili).
170. *On sharp Olsen’s and trace inequalities for multilinear fractional integrals, Potential Analysis, https://doi.org/10.1007/s11118-022-09991-y (with L. Grafakos).
171. *On some extrapolation in generalized grand Morrey spaces and applications to PDEs, Electronic Research Archive, 2023 (accepted). (with E. Gordadze and M. A. Ragusa).
172. *Extrapolation in new weighted grand Morrey Spaces beyond the Muckenhoupt classes, J. Math.l Anal. App., 2023, https://doi.org/10.1016/j.jmaa.2023.127181.
173. *A complete characterization of the generalized multilinear Sobolev inequality in grand product Lebesgue spaces defined on non-homogeneous spaces, Results in Mathematics, Published Online, DOI: 10.1007/s00025-023-01959-7 (with V. Kokilashvili).
174. *Boundedness of operators of harmonic analysis in grand variable exponent Morrey spaces. Mediterr. J. Math. 20 (2023), no. 2, Paper No. 71, 25 pp.; https://doi.org/10.1007/s00009-023-02267-8 (with V. Kokilashvili).
175. Boundedness weighted criteria for multilinear Riemann-Liouville integral operators, Trans. A. Razmadze Math. Inst. 177 (2023), no. 1, 147-148,
176. Duality
and interpolation for weighted grand Morrey spaces, Trans. A. Razmadze Math.
Inst. 177 (2023), no. 1, 149-155 (with H. Rafeiro and T. Tsanava).