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Sibirskii Matematicheskii Zhurnal, 2023, Volume 64, Number 1, Pages 40–55
DOI: https://doi.org/10.33048/smzh.2023.64.104 (Mi smj7743) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Polynomial approximation with respect to multiplicative systems in the Morrey space

S. S. Volosivets

Saratov State University
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DOI: https://doi.org/10.33048/smzh.2023.64.104
Abstract: We establish the main theorems on polynomial approximation with respect to multiplicative systems in the Morrey space and estimate the best approximations and the moduli of smoothness of functions in terms of the growth of the generalized derivatives of their best approximation polynomials, Fourier sums, and Riesz–Zygmund means with respect to multiplicative systems. Also, we provide some criteria for a function to belong to the classes with prescribed majorants for the modulus of smoothness or best approximation in the Morrey space.
Keywords: Morrey space, multiplicative system, $K$-functional, generalized derivative, direct and inverse approximation theorems.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation FSRR-2020-0006
The author was supported by the Ministry of Science and Higher Education of the Russian Federation (Project FWNF–2020–0006).
Received: 09.03.2022
Revised: 07.06.2022
Accepted: 15.06.2022
English version:
Siberian Mathematical Journal, 2023, Volume 64, Issue 1, Pages 33–47
DOI: https://doi.org/10.1134/S0037446623010044
Bibliographic databases:
Document Type: Article
UDC: 517.518.3
MSC: 35R30
Language: Russian
Citation: S. S. Volosivets, “Polynomial approximation with respect to multiplicative systems in the Morrey space”, Sibirsk. Mat. Zh., 64:1 (2023), 40–55; Siberian Math. J., 64:1 (2023), 33–47
Citation in format AMSBIB
\Bibitem{Vol23}
\by S.~S.~Volosivets
\paper Polynomial approximation with respect to multiplicative systems in the Morrey space
\jour Sibirsk. Mat. Zh.
\yr 2023
\vol 64
\issue 1
\pages 40--55
\mathnet{http://mi.mathnet.ru/smj7743}
\crossref{https://doi.org/10.33048/smzh.2023.64.104}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4554799}
\transl
\jour Siberian Math. J.
\yr 2023
\vol 64
\issue 1
\pages 33--47
\crossref{https://doi.org/10.1134/S0037446623010044}
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    • This publication is cited in the following 1 articles:
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