Remarks on the uniform and L1-convergence of trigonometric series

被引：0

作者：

P. Kórus

机构：

[1] University of Szeged,Bolyai Institute

来源：

Acta Mathematica Hungarica | 2010年 / 128卷

关键词：

sine series; Fourier series; -convergence; uniform convergence; monotonicity; general monotone; supremum bounded variation; 42A20; 42A32;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

Chaundry and Jolliffe [1] proved that if ak is a nonnegative sequence tending monotonically to zero, then a necessary and sufficient condition for the uniform convergence of the series Σk=1∞ak sin kx is limk→∞kak = 0. Lately, S. P. Zhou, P. Zhou and D. S. Yu [4] generalized this classical result. In this paper we propose new classes of sequences for which we get the extended version of their results. Moreover, we generalize the results of S. Tikhonov [2] on the L1-convergence of Fourier series.

引用

页码：369 / 380

页数：11

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