V. M. Kokilashvili, A. N. Meskhi, “Weighted extrapolation in Iwaniec–Sbordone spaces. Applications to integral operators and approximation theory”, Function spaces, approximation theory, and related problems of mathematical analysis, Collected papers. In commemoration of the 110th anniversary of Academician Sergei Mikhailovich Nikol'skii, Trudy Mat. Inst. Steklova, 293, MAIK Nauka/Interperiodica, Moscow, 2016, 167–192; Proc. Steklov Inst. Math., 293 (2016), 161

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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2016, Volume 293, Pages 167–192
DOI: https://doi.org/10.1134/S0371968516020126 (Mi tm3712)

This article is cited in 17 scientific papers (total in 17 papers)

Weighted extrapolation in Iwaniec–Sbordone spaces. Applications to integral operators and approximation theory

V. M. Kokilashvili, A. N. Meskhi

A. Razmadze Mathematical Institute, I. Javakhishvili Tbilisi State University, 6, Tamarashvili Str., 0177 Tbilisi, Georgia

Full-text PDF (301 kB) Citations (17)

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DOI: https://doi.org/10.1134/S0371968516020126

Abstract: We prove extrapolation theorems in weighted Iwaniec–Sbordone spaces and apply them to one-weight inequalities for several integral operators of harmonic analysis. In addition, in weighted grand Lebesgue spaces, we establish Bernstein and Nikol'skii type inequalities and prove direct and inverse theorems on the approximation of functions.

Funding agency	Grant number
Shota Rustaveli National Science Foundation	D/13-23 31/47
This work was supported by the Shota Rustaveli National Science Foundation, project nos. D/13-23 and 31/47.

Received: September 10, 2015

English version:
Proceedings of the Steklov Institute of Mathematics, 2016, Volume 293, Pages 161–185
DOI: https://doi.org/10.1134/S008154381604012X

Bibliographic databases:

Document Type: Article

UDC: 517.51

Language: Russian

Citation: V. M. Kokilashvili, A. N. Meskhi, “Weighted extrapolation in Iwaniec–Sbordone spaces. Applications to integral operators and approximation theory”, Function spaces, approximation theory, and related problems of mathematical analysis, Collected papers. In commemoration of the 110th anniversary of Academician Sergei Mikhailovich Nikol'skii, Trudy Mat. Inst. Steklova, 293, MAIK Nauka/Interperiodica, Moscow, 2016, 167–192; Proc. Steklov Inst. Math., 293 (2016), 161–185

Citation in format AMSBIB

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Linking options:

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https://doi.org/10.1134/S0371968516020126

https://www.mathnet.ru/eng/tm/v293/p167

This publication is cited in the following 17 articles:

Alexander Meskhi, “EXTRAPOLATION IN GRAND BANACH FUNCTION SPACES”, J Math Sci, 2025
Alexander Meskhi, “Extrapolation in new weighted grand Morrey spaces beyond the Muckenhoupt classes”, Journal of Mathematical Analysis and Applications, 529:2 (2024), 127181
B. I. Golubov, S. S. Volosivets, “Approximation by Haar and Walsh Polynomials in Weighted Generalized Grand Lebesgue Space”, J. Contemp. Mathemat. Anal., 59:3 (2024), 151
Vakhtang Kokilashvili, Alexander Meskhi, Humberto Rafeiro, Stefan Samko, Operator Theory: Advances and Applications, 298, Integral Operators in Non-Standard Function Spaces, 2024, 99
Vakhtang Kokilashvili, Alexander Meskhi, Humberto Rafeiro, Stefan Samko, Operator Theory: Advances and Applications, 298, Integral Operators in Non-Standard Function Spaces, 2024, 247
Kokilashvili V., Meskhi A., “Extrapolation and the Boundedness in Grand Variable Exponent Lebesgue Spaces Without Assuming the Log-Holder Continuity Condition, and Applications”, J. Fourier Anal. Appl., 28:2 (2022), 28
V. M. Kokilashvili, A. N. Meskhi, “On the Boundedness of Integral Operators in Weighted Grand Morrey Spaces”, Proc. Steklov Inst. Math., 312 (2021), 194–206
V. Kokilashvili, A. Meskhi, “Maximal and singular integral operators in weighted grand variable exponent Lebesgue spaces”, Ann. Funct. Anal., 12:3 (2021), 48
S. M. Umarkhadzhiev, “On elliptic homogeneous differential operators in grand spaces”, Russian Math. (Iz. VUZ), 64:3 (2020), 57–65
Kokilashvili V., Meskhi A., “Extrapolation in Weighted Classical and Grand Lorentz Spaces. Application to the Boundedness of Integral Operators”, Banach J. Math. Anal., 14:3 (2020), 1111–1142
V. Kokilashvili, “On the boundedness in generalized weighted grand Lebesgue spaces of some integral operators associated to the Schrodinger operator”, Trans. A Razmadze Math. Inst., 174:3 (2020), 419–421
V. Kokilashvili, A. Meskhi, M. A. Ragusa, “Weighted extrapolation in grand Morrey spaces and applications to partial differential equations”, Rend. Lincei-Mat. Appl., 30:1 (2019), 67–92
V. Kokilashvili, “Approximation by trigonometric polynomials in the framework of weighted fully measurable grand Lorentz spaces”, Trans. A Razmadze Math. Inst., 173:3 (2019), 161–162
V. M. Kokilashvili, “Weighted grand Lebesgue space with a mixed norm and integral operators”, Dokl. Math., 100:3 (2019), 549–550
V. Kokilashvili, A. Meskhi, “Extrapolation results in grand Lebesgue spaces defined on product sets”, Positivity, 22:4 (2018), 1143–1163
S. M. Umarkhadzhiev, “Description of the Space of Riesz Potentials of Functions in a Grand Lebesgue Space on $\mathbb{R}^n$ ”, Math. Notes, 104:3 (2018), 454–464
V. M. Kokilashvili, A. N. Meskhi, “Extrapolation in Grand Lebesgue Spaces with $A_{\infty}$ Weights”, Math. Notes, 104:4 (2018), 518–529

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Труды Математического института имени В. А. Стеклова

Proceedings of the Steklov Institute of Mathematics

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