一般单调傅里叶系数函数

IF 1.4 4区数学 Q1 MATHEMATICS

Russian Mathematical Surveys Pub Date : 2021-01-01 DOI:10.1070/RM10003

Aleksandr Sergeevich Belov, M. Dyachenko, Sergei Yur'evich Tikhonov

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引用次数: 5

摘要

本文研究了一类具有一般单调系数的三角级数。证明了可积连续函数的傅里叶系数的尖锐估计。还得到了傅里叶级数各种收敛类型的系数的最优结果。对于具有-系数的级数和的光滑性的-模，以及在Lebesgue, Lorentz, Besov和Sobolev空间中这些和的(拟)范数的傅里叶系数的双边估计。参考书目:99个标题。

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Functions with general monotone Fourier coefficients

This paper is a study of trigonometric series with general monotone coefficients in the class with . 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 two-sided estimates are obtained for the -moduli of smoothness of sums of series with -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.

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来源期刊

Russian Mathematical Surveys 数学-数学

CiteScore

1.70

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Russian Mathematical Surveys is a high-prestige journal covering a wide area of mathematics. The Russian original is rigorously refereed in Russia and the translations are carefully scrutinised and edited by the London Mathematical Society. The survey articles on current trends in mathematics are generally written by leading experts in the field at the request of the Editorial Board.