A. S. Belov, M. I. Dyachenko, S. Yu. Tikhonov, “Functions with general monotone Fourier coefficients”, Russian Math. Surveys, 76:6 (2021), 951

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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. Belov^a, M. I. Dyachenko^b, S. Yu. Tikhonov^cde

^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) Russian version article

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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

GM (p)

$\operatorname{GM}(p)$ 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

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”, Russian Math. Surveys, 76:6 (2021), 951–1017

Citation in format AMSBIB

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\paper Functions with general monotone Fourier coefficients

\jour Russian Math. Surveys

\yr 2021

\vol 76

\issue 6

\pages 951--1017

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\crossref{https://doi.org/10.1070/RM10003}

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Linking options:

https://www.mathnet.ru/eng/rm10003

https://doi.org/10.1070/RM10003

https://www.mathnet.ru/eng/rm/v76/i6/p3

This publication is cited in the following 5 articles:

B. V. Simonov, A. A. Jumabayeva, “On relations between partial moduli of smoothness in mixed metrics”, Period Math Hung, 88:1 (2024), 38
M. I. Dyachenko, A. P. Solodov, “Asymptotics of sums of sine series with fractional monotonicity coefficients”, Anal. Math., 49:1 (2023), 67
Yu. Krotova, S. Volosivets, “Fourier transforms and fractional Lipschitz and Nikol’skii classes in uniform metric”, Acta Math. Hungar., 169:1 (2023), 57
M. Saucedo, “Hardy inequalities for $p$ -weakly monotone functions”, Eurasian Math. J., 14:2 (2023), 94–106
M. I. Dyachenko, “Uniform Convergence of Sine Series with Fractional-Monotone Coefficients”, Math. Notes, 114:3 (2023), 296–302

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

Statistics & downloads:
Abstract page:	603
Russian version PDF:	136
English version PDF:	105
Russian version HTML:	107
References:	104
First page:	55

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