Functions with general monotone Fourier coefficients

A. S. Belov   ; M. I. Dyachenko   ; S. Yu. Tikhonov

Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 76 (2021) no. 6, pp. 951-1017

Résumé

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 $1$ 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.

Détail

Keywords: functions with general monotone Fourier coefficients; estimates of Fourier coefficients; moduli of smoothness; Lebesgue, Lorentz
Mots-clés : Besov, Sobolev spaces.

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