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Matematicheskie Zametki, 2021, Volume 109, Issue 1, Pages 27–35
DOI: https://doi.org/10.4213/mzm12796 (Mi mzm12796) 		 
Criteria for a Function to Belong to the $p$-Variational Besov Space

S. S. Volosivets, S. A. Krayukhin

Saratov State University
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DOI: https://doi.org/10.4213/mzm12796
Abstract: Necessary and sufficient conditions for a function to belong to the Besov space constructed from the space $V_p$ of functions of bounded $p$-variation are studied. These conditions are expressed in terms of approximations of functions by Fourier partial sums and Fejér means, as well as in terms of the norms of the derivatives of the approximating polynomials in $V_p$.
Keywords: Besov space, Fourier partial sums, Fejér means.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation FSRR-2020-0006
This work was supported by the Ministry of Science and Higher Education of the Russian Federation (project no. FSRR-2020-0006).
Received: 25.03.2020
Revised: 08.07.2020
English version:
Mathematical Notes, 2021, Volume 109, Issue 1, Pages 21–28
DOI: https://doi.org/10.1134/S000143462101003X
Bibliographic databases:
Document Type: Article
UDC: 517.518
PACS: 517.518.83
Language: Russian
Citation: S. S. Volosivets, S. A. Krayukhin, “Criteria for a Function to Belong to the $p$-Variational Besov Space”, Mat. Zametki, 109:1 (2021), 27–35; Math. Notes, 109:1 (2021), 21–28
Citation in format AMSBIB
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