On the convergence in mean of trigonometric Fourier series

被引：0

作者：

Belov, A. S. ^{[1
]}

机构：

[1] Ivanovo State Univ, Ivanovo, Russia

来源：

MATHEMATICAL NOTES | 2010年 / 87卷 / 3-4期

基金：

俄罗斯基础研究基金会;

关键词：

trigonometric Fourier series; 2 pi-periodic function; convergence in mean; Zygmund's theorem; Abel transformation; Dirichlet kernel;

D O I：

10.1134/S0001434610030247

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove the sharpness of Zygmund's theorem, which asserts that if a 2 pi-periodic function f belongs to L ln(+) L, then its Fourier series is convergent in mean.

引用

页码：466 / 474

页数：9

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