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.
2. Positions:
a) 11.05.2000- up to now : Senior Researcher (Associate Professor) of A.Razmadze Mathematical Institute, Georgia.
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 of A.
Razmadze Mathematical Institute, Georgia.
3. Mailing Addresses:
A. Razmadze Mathematical Institute, 1, M. Aleksidze Str., 0193 Tbilisi, Georgia.
4. Languages:
Georgian (Mother), Russian, English, Italian.
5. Education:
a) 1995-1998 - Post-graduate Student of A.
Razmadze Mathematical Institute
b) 1990-1995 - Student of the Georgian Technical University.
6. Academic 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". Georgian Technical University,
(Supervisor Prof. V. Kokilashvili).
7. Main Research Field:
Harmonic Analysis and Applications in Partial Differential Equations.
8. 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.
9. Research Grants:
a) 01.01.2008- 01.01.2010: Georgian National
Foundation Grant “Some Topics of Harmonic and Non-linear Analysis in Non-standard
Setting with Applications in Differential Equations” No. GNSF/STO7/3-169
b) 01.01.2007-01.01.2009: INTAS grant : “Variable Exponent Analysis”,
Nr.06-1000017-8792.
c) 2006-2008: Georgian National Science Foundation Grant, “Nonstandard
function spaces and functions with applications to partial differential equations”,
No. GNSF/ST06/3-010.
d) 01.09. 2006-01.09.2008: INTAS grant: “Function spaces and applications
to partial differential equations”, No. 05-1000008-8157.
e) 1998, 2000-2004, 2006-up to now: Georgian President’s Grant for Young
Scientists.
f) 2001-2002: An INTAS Fellowship grant for Young Scientists (Fellowship Reference
No YSF 01/1-8).
g) 2000: Euler grant of the German Mathematical Society for Young Mathematicians
h) 1999, 2001: Grant of the Royal Society (UK).
i) 1999-2003: Grant of the Georgian Academy of Sciences No. 1.7.
j) 1997-1998: J. Soros Grant for Post-graduate Students.
10. Awards:
1) 2002, Prize of the Union of Georgian Mathematicians for the Best Scientific
Works.
2) 1995, Diploma for winning the first place in the students' republican scientific-technological
conference.
11. Participation in conferences:
1) “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.
2) “Boundedness of one-sided operators in variable exponent Lebesgue spaces”,
Workshop and Konference In Function Spaces, Differential Operators and Nonlinear
Analysis, Helsinki, Finland, August 22-29, 2008.
3) 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 0perators and
Their Applications”, Astana, Kazakhstan, September 3-5, 2007.
4) “On the boundedness of one-sided singular integrals in Lebesgue spaces
with variable exponent”, 6-th International ISAAC Congress, Ankara, Turkey,
13-18 August, 2007.
5) “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.
6) “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.
7) “ 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.
8) “ 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.
9) "Stime a due pesi per funzioni massimali forti e potenziali con nuclei
multipli". XXV Conferenza di Analisi Armonica, Universita` di Bologna,
Dipartimento di Matematica, 6-9 , aprile 2005, Organizzatore: Nicola Arcozzi.,
6-9 Aprile 2005.
10) "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.
11) "Fractional integrals on nonhomogeneous spaces ", 7th International
Conference on Harmonic Analysis and Partial Differential Equations, El Escorial,
Madrid (Spain) June 21-25, 2004.
12) "Criteri di limitatezza per operatori potenziali con nuclei prodotto"
XXIV Convegno Nazionale di Analisi Armonica (Italia) , Sestri Levante, 29 Marzo
- 1 Aprile, 2004.
13) “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.
14) “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. Meskhi and S. Samko, September 8-13,
2003.
15) “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.
16) “On a measure of non-compactness formaximal functions”, Congress
of Georgian Mathematicians, Tbilisi, Georgia, 11-13 October, 2001.
17) “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.
18) “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.
19) “Weighted problems for higher dimensional singular integrals via Clifford
analysis”, NATO Advanced Workshop " Clifford Analysis and its Applications",
Prague, October 30- November 3, 2000.
20) "Boundedness and compactness weighted criteria for the operators with
positive kernels". European Congress for Mathematics, Barcelon, July 10-14,
2000.
21) " 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.
22) “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.
23) " Weighted Inequalities for the Riemann- Liouvlille and Weyl operators
defined on SHT", International Congress of Mathematicians, Berlin, Germany,
August 18-27, 1998;
24) " Boundedness and compactness criteria for the Riemann- Liouville and
Weyl transforms", International Conference in Nonlinear Analysis, Function
Spaces and Applications 6, Prague, May 31- June 6, 1998;
25) “Two-weight estimates for singular integrals”, Congress of Georgian
Mathematicians, Tbilisi, Georgia, September, 1997.
12. Scientific
and Academic Visits:
a) 2008 (January 15- March 15) University of Padova, Italy.
b) 2006 (November 25- December 5) University of Pisa, Italy.
c) 2006 (July 2- July 15), University of Sussex, UK.
d) 2005 (June 1- September 1), Department of Mathematics, University of Pisa,
Italy.
e) 2005 (January 23- February 4), University of Sussex (UK).
f) 2004 (November), University of Naples, department of mathematics (Italy).
g) 2002 (June-July), University of Sussex (UK).
h) 2001 (April), University of Sussex (UK);
i) 1999 (March), University of Sussex, Cardiff University (UK);
j) 1998 (June 1- 7), Mathematical Institute of the Czech Republic.
13. Talks in Seminars:
a) 11.12.2006. “Criteri per la limitatezza dei potenziali ed integrali
singolari negli spazi di Lebesgue con l’esponente variabile”. University
of Pisa, Italy, (Head of the Seminar Prof. Vladimir Georgiev).
b) 05.12.2006. “Two-weight inequalities for potential operators and some
applications”. Department of Mathematics, University of Padova, Italy,
(Head of the Seminar Prof. Massimo Lanza de Cristoforis).
c) 27.05.2005: "On a trace inequality for potentials and applications in
the solvability of non-linear integral equations and the spectral theory of
integral operators", Department of Mathematics, University of Pisa, Italy,
(Head of the Seminar Prof. V. Georgiev).
d) 11.11.2004:"Two-weight estimates for multiple Hardy-type transforms
and some applications", Scuola normale Superiore, Italy (Head of the Seminar
Prof. Fulvio Ricci).
e) 12.01.2004, 26.01.2004: Two-weight inequalities for potential operators and
some applications, Scuola Normale Superiore, Pisa, Italy, (Head of the Seminar
Prof. Fulvio Ricci).
f) 30.03. 1999: " Boundedness and compactness criteria for one-sided potentials",
University of Wales, UK, (Head of the Seminar Prof. W.D.Evans).
g) 11.06.1998: "Boundedness and compactness criteria for the Riemann-Liouville
Transforms", Mathematical Institute of the Academy of Sciences of Czech
Republic, (Head of the Seminar Professor Alois Kufner).
14. Teaching:
a) 15.01.2008- 15.03.2008: University of Padova, Italy (Course “Inequalities
of Real Analysis”).
b) 2006- up to now: School of Mathematical Sciences, GC University, Lahore,
Pakistan (Courses of Functional Analysis, Measure Theory, Complex Analysis for
PhD Students).
c) 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).
d) 2001-2002: Tbilisi State University, Georgia, (Ordinary Differential Equations,
Faculty of Differential Equations).
e) Experience in Working with PhD Students.
15. 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 33 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. Professor W.D. Evans, Address: Cardiff School of Mathematics, Cardiff University,
23 Senghennydd Road, Cardiff CF24 4AG, WALES, UK, Tel. (+44) 029 2087 4827 ;
Fax: (+44) 029 2087 4199, e-mail: EvansWD@cf.ac.uk
6. Professor Fulvio Ricci, Scuola Normale Superiore, Piazza dei Cavallieri 7,
56126 Pisa, Italy, Telephone: +39-050-509257, e-mail: fricci@sns.it.
7. 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
Publications of Alexander Meskhi
1. Monograph:
Bounded and Compact Integral Operators, Kluwer Academic Publishers, Dordrecht, Boston, London, 2002 (With D. E. Edmunds and V. Kokilashvili).
2. Papers in Proceedings of Conferences:
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)
• 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) .
• 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.), Kluwer Academic Publishers, Dordrecht (The Netherlands), 2001
(with V. Kokilashvili).
• 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, New York, Bazel, Marcell Dekker, 2000
(with V. Kokilashvili).
3. Papers in Refereed Journals:
• Two-weight estimates for strong fractional
maximal functions and potentials with multiple kernels. J. Korean Math. Soc.
(accepted for publication) (with V. Kokilashvili).
•Boundedness criteria for maximal functions and potentials on the half-space
in weighted Lebesgue spaces with variable exponents. Integr. Transf. Spec. Func.
(to appear) (with M. Asif and V. Kokilashvili).
• One-sided operators in $L^{p(x)}$ spaces. Math. Nachr. 281(2008), No.
11, 1525–1548 (with D. E. Edmunds and V. Kokilashvili)
• On a measure of non-compactness for maximal and potential operators
J. Inequal. Appl. 2008, Art. ID 697407, 19 pages (with M. Asif)
• Boundedness and compactness of positive integral operators on cones
of homogeneous groups, Positivity (accepted for publication) (with U. Ashraf
and M. Asif).
• Boundedness of Maximal and Singular Operators in Morrey Spaces with
Variable Exponent, Armenian Journal of Mathematics 1(2008), No.1, 18-28 (with
V. Kokilashvili).
• Weight characterization of the trace inequality for the generalized
Riemann-Liouville transform in $L^{p(x)}$ spaces, Math. Ineq. Appl. (accepted
for publication) (with U. Ashraf and V. Kokilashvili).
•Two-weight estimates in $L^{p(\cdot)}$ spaces with applications to Fourier
Series. Houston Journal of Mathematics (accepted for publication) (with D. E.
Edmunds and V. Kokilashvili).
•On an Essential Norm for the Hilbert Transforms in $L^{p(x)}$ Spaces,
Georgian Math. J. 15(2008), No.2, 208-223 (with M. Asif).
• 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).
•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).
• On the measure of non-compactness for some classical operators. Acta
Math. Sinica. 22(6)(2006), 1847-1862. (with D. E. Edmunds and A. Fiorenza).
• A note on two-weight inequalities for multiple Hardy-type operators,
J. Funct. Spaces Appl. 3(2005), 223-237.
• On some two-weight inequalities for fractional integrals on nonhomogeneous
spaces, Z. Anal. Anwend. 24(2005), No.4, 871-885 (With V. Kokilashvili).
• On one-sided potentials with multiple kernels. Integral Transf. Spec.
Funct. 16 (2005), No. 8, 669--683.(with V. Kokilashvili).
• 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).
• On a trace inequality for one-sided potentials with multiple kernels.
Frac. Calc. Appl. Anal. 6(2003), No.4, 461- 472 (with V. Kokilashvili)
•. On the inversion and characterization of the Riesz potentials in the
weighted Lebesgue spaces. Memoirs Diff. Equation Math. Phys. 29(2003), 31-45.
(With V. Kokilashvili and S. Samko)
• On a measure of non-compactness for singular integrals. J. Function
Spaces Appl. 1(2003), No.1, 35-43.
• 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).
• On a measure of non-compactness for maximal operators. Math. Nachr.
254-255 (2003), 97-106. (with D.E. Edmunds).
• Weight inequalities for one-sided potentials for critical weights. Fract.
Calc. Appl. Anal. 25(2002),255-265 (with V. Kokilashvili).
• Potential-type operators in $L^{p(x)}$ spaces, Z. Anal. Anwend., 21(2002),
681-690 (with D.E. Edmunds).
• 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).
• On Fourier multipliers in weighted Triebel-Lizorkin spaces, J. Inequal.
Appl. 7(2002), No. 4, 555-591 (with. D.E.Edmunds and V. Kokilashvili) .
• On the singular numbers for some integral operators. Revista Mat. Compl.
14(2001), No.2, 379-393.
• Fractional integrals on measure spaces, Fract. Calc. Appl. Anal. 4(2001),
No.1. 1-24 ( With V. Kokilashvili).
• Criteria of the boundedness and compactness for generalized one-sided
potentials. Real Anal. Exchange 26(2000/2001), No.1, 217- 236.
• 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).
• Asymptotic behavior of singular and entropy numbers for some Riemann-Liouville
type operators. Georgian Math. J. 8(2001), No.2., 323- 332.
• Weight inequalities for singular integrals defined on homogeneous and
nonhomogeneous type spaces. Georgian Math. J. 8(2001), No. 1, 33-59 (with D.
E. Edmunds and V. Kokilahsvili).
• Criteria for the boundedness and compactness of operators with positive
kernels, Proc. Edinburgh Math. Soc. 44(2001), 267-284.
• Criteria for the boundedness and compactness of operators with power-logarithmic
kernels. Analysis Math. 27(2001), No.2, 173- 185 (with V. Kokilashvili).
• 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).
• Two-weight estimates for singular integrals defined on homogeneous type
spaces. Canadian J. Math. 52(2000), No. 3, 468-502 (with D. E. Edmunds and V.
Kokilashvili).
• On the boundedness and compactness of ball fractional integral operators.
Fract. Calc. Appl. Anal. 3 (2000), No.1, 13-30.
• 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).
• 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).
• Two-weight inequalities for a discrete Hilbert transform. Proc. A. Razmadze
Math. Inst. Georgian Acad. Sci. 116(1998), 107- 122. (with I. Gabisonija).
• Solution of some weight problems for the Riemann-Liouville and Weyl
operators. Georgian Math. J. 5(1998), No.6, 265-274.
• Koosis type theorems for singular integrals and potentials defined on
homogeneous groups. Proc. A. Razmadze Math. Inst. 114(1997), 59- 70.
• Two-weight inequalities for potentials defined on homogeneous groups.
Proc. A. Razmadze Math. Inst. 112(1997), 91- 111.
• 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).
• Weighted inequalities for the Hilbert transform and multipliers of Fourier
transforms. J. Inequal. Appl. 1( 1997), No. 3, 239- 252 (with V. Kokilashvili).
• Two-weight estimates 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).
4. Short Papers in Refereed Journals:
•Maximal and potential operators in variable
Morrey spaces defined on non-homogeneous spaces. Bull. of the Georgian National
Academy of Sci. (accepted) (with V. Kokilashvili).
•On the maximal and Fourier operators in weighted Lebesgue spaces with
variable exponent, 146 (2008), 120-123 (with V. Kokilashvili)
•Two-weight estimates for maximal functions in $L^{p(x)}$ spaces, Proc.
A. Razmadze Math. Inst. 145(2007) , 100-102 (with V. Kokilashvili).
•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).
•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).
• 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), 135-140. (with D. Edmunds and
V. Kokilashvili).
• On a weighted Strichartz estimate for inhomogeneous wave equations.
Proc. A. Razmadze Math. Inst. 139(2005), 96-99 (with V. Georgiev).
• 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).
• A Note 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).
• Two-weight inequalities for multiple Hardy-type operators. Proc. A.
Razmadze math. Inst. 136(2004), 149-153.
• On a measure of non-compactness for the Riesz transforms. Proc. A. Razmadze
Math. Inst. 129 (2002), 156—157.
• On the boundedness and compactness criteria for the Riemann-Liouville
type discrete operator. Proc. A. Razmadze Math. Inst. 126(2001), 117-119.
• 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).
• Boundedness and compactness criteria for the generalized Riemann-Liouville
operator. Proc. A. Razmadze Math. Inst. 121(1999), 161-162.
• On the measure of non-compactness and singular numbers for the Volterra
integral operators. Proc. A. Razmadze Math. Inst. 123(2000), 162-164.
• Two-weight inequalities for a discrete Hardy operators and Hilbert transform.
Bull. Acad. Sci. Georgia 158(1998), No. 2, 191-193 (with I. Gabisonija).
• Weighted inequalities for Riemann-Liouville transform, Proc. A. Razmadze
Math. Inst. 117(1998), 151-153.
• Boundedness and compactness weighted criteria for Riemann-Liouville
and one-sided maximal operators. Proc. A. Razmadze Math. Inst. 117(1998),126-128.
• 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).
• Two-weight inequalities for potentials on the Lorentz spaces defined
on homogeneous groups. Proc. A. Razmadze Math. Inst. 112(1997), 148-150.
• Two-weight inequalities for singular integrals on the Lorentz spaces
defined on homogeneous groups. Proc. A. Razmadze Math. Inst. 112(1997), 141-143
(with V. Kokilashvili).
• 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).
• Two- weight inequalities for potentials on homogeneous groups. Bull.
Acad. Sci. Georgia 154(1996), No 3. 353-355.
• Two-weight inequalities for singular integrals on Heisenberg groups.
Bull. Acad. Sci. Georgia 153(1996), No.1 34-36.
5. Preprints and Submitted Papers:
• Morrey spaces and fractional integral
operators (with Eridani and V. Kokilashvili) Preprint No.65, School of Mathematical
Sciences. Lahore.
•Variable exponent morrey spaces on non-doubling quasimetric measure spaces:
maximal and potential operators (with V. Kokilashvili).