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Sbornik: Mathematics, 2019, Volume 210, Issue 7, Pages 994–1018
DOI: https://doi.org/10.1070/SM9096 (Mi sm9096) 		 
This article is cited in 10 scientific papers (total in 10 papers)

Smoothness of functions and Fourier coefficients

M. I. Dyachenkoa, A. B. Mukanovbcd, S. Yu. Tikhonovceb

a Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, Russia
b Departament de Matemàtiques, Universitat Autònoma de Barcelona, Bellaterra (Barcelona), Spain
c Centre de Recerca Matemàtica, Bellaterra (Barcelona), Spain
d Kazakhstan Branch of Lomonosov Moscow State University, Astana, Kazakhstan
e Institució Catalana de Recerca i Estudis Avançats, Barcelona, Spain
English version PDF (609 kB) Citations (10)
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DOI: https://doi.org/10.1070/SM9096
Abstract: We consider functions represented as trigonometric series with general monotone Fourier coefficients. The main result of the paper is the equivalence of the $L_p$ modulus of smoothness, $1<p<\infty$, of such functions to certain sums of their Fourier coefficients. As applications, for such functions we give a description of the norm in the Besov space and sharp direct and inverse theorems in approximation theory.
Bibliography: 34 titles.
Keywords: Fourier series, general monotone sequences, moduli of smoothness.
Funding agency Grant number
Russian Foundation for Basic Research 19-01-00457-a
Ministry of Education and Science of the Republic of Kazakhstan AP05132590
AP05132071
Ministerio de Ciencia e Innovación de España MTM2017-87409-P
Generalitat de Catalunya 2017 SGR 358
M. I. Dyachenko's research was partially supported by the Russian Foundation for Basic Research (grant no. 19-01-00457-a) and the Ministry of Education and Science of the Republic of Kazakhstan (grant no. AP05132590). A. B. Mukanov's research was supported by the Ministry of Education and Science of the Republic of Kazakhstan (grant no. AP05132071). S. Yu. Tikhonov's research was partially supported by Ministerio de Ciencia, Innovación y Universidades (grant no. MTM2017-87409-P) and Generalitat de Catalunya (2017 SGR 358).
Received: 08.03.2018 and 06.12.2018
Russian version:
Matematicheskii Sbornik, 2019, Volume 210, Number 7, Pages 94–119
DOI: https://doi.org/10.4213/sm9096
Bibliographic databases:
Document Type: Article
UDC: 517.518.4+517.518.83
MSC: Primary 42A32; Secondary 26A16, 42A16, 46E35
Language: English
Original paper language: Russian
Citation: M. I. Dyachenko, A. B. Mukanov, S. Yu. Tikhonov, “Smoothness of functions and Fourier coefficients”, Mat. Sb., 210:7 (2019), 94–119; Sb. Math., 210:7 (2019), 994–1018
Citation in format AMSBIB
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    • This publication is cited in the following 10 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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