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Russian Mathematical Surveys, 2021, Volume 76, Issue 6, Pages 951–1017
DOI: https://doi.org/10.1070/RM10003 (Mi rm10003) 		 
This article is cited in 5 scientific papers (total in 5 papers)

Functions with general monotone Fourier coefficients

A. S. Belova, M. I. Dyachenkob, S. Yu. Tikhonovcde

a Ivanovo State University
b Lomonosov Moscow State University, Moscow Center for Fundamental and Applied Mathematics
c Centre de Recerca Matemàtica, Barcelona, Spain
d Institució Catalana de Recerca i Estudis Avançats, Barcelona, Spain
e Universitat Autònoma de Barcelona, Barcelona, Spain
English version PDF (984 kB) Citations (5)
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DOI: https://doi.org/10.1070/RM10003
Abstract: This paper is a study of trigonometric series with general monotone coefficients in the class $\operatorname{GM}(p)$ with $p\geqslant 1$. Sharp estimates are proved for the Fourier coefficients of integrable and continuous functions. Also obtained are optimal results in terms of coefficients for various types of convergence of Fourier series. For $1<p<\infty$ two-sided estimates are obtained for the $L_p$-moduli of smoothness of sums of series with $\operatorname{GM}(p)$-coefficients, as well as for the (quasi-)norms of such sums in Lebesgue, Lorentz, Besov, and Sobolev spaces in terms of Fourier coefficients.
Bibliography: 99 titles.
Keywords: functions with general monotone Fourier coefficients; estimates of Fourier coefficients; moduli of smoothness; Lebesgue, Lorentz, Besov, Sobolev spaces.
Funding agency Grant number
Russian Science Foundation 21-11-00131
Ministry of Education and Science of the Republic of Kazakhstan AP08856479
AP09260052
Ministerio de Ciencia e Innovación de España PID2020-114948GB-I00
Generalitat de Catalunya 2017 SGR 358
Agencia Estatal de Investigacion CEX2020-001084-M
The work on Theorems 2.9, 2.12, 4.1(B), and Lemma 4.6 was conducted by the second author under a grant of the Russian Science Foundation (project no. 21-11-00131), at the Lomonosov Moscow State University. The research of the third author was supported by PID2020-114948GB-I00, 2017 SGR 358, and the Severo Ochoa and María de Maeztu Program for Centers and Units of Excellence in R&D (CEX2020-001084-M). This work was also supported by the Ministry of Education and Science of the Republic of Kazakhstan (grants nos. AP08856479 and AP09260052).
Received: 21.04.2021
Russian version:
Uspekhi Matematicheskikh Nauk, 2021, Volume 76, Issue 6(462), Pages 3–70
DOI: https://doi.org/10.4213/rm10003
Bibliographic databases:
Document Type: Article
UDC: 517.5
MSC: Primary 42A16, 42A32; Secondary 42A10, 42A20, 46E35
Language: English
Original paper language: Russian
Citation: A. S. Belov, M. I. Dyachenko, S. Yu. Tikhonov, “Functions with general monotone Fourier coefficients”, Uspekhi Mat. Nauk, 76:6(462) (2021), 3–70; Russian Math. Surveys, 76:6 (2021), 951–1017
Citation in format AMSBIB
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