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
收藏
页码：466 / 474
页数：9
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