Integrability and continuity of functions represented by trigonometric series: coefficients criteria

被引：36

作者：

Dyachenko, Mikhail ^{[1
]}

Tikhonov, Sergey ^{[2
,3
]}

机构：

[1] Moscow MV Lomonosov State Univ, Moscow 119992, Russia

[2] ICREA, Barcelona 08193, Spain

[3] Ctr Recerca Matemat, Barcelona 08193, Spain

来源：

STUDIA MATHEMATICA | 2009年 / 193卷 / 03期

关键词：

trigonometric series; weighted integrability; uniform convergence; generally monotone sequences; trigonometric approximation; GENERAL MONOTONE COEFFICIENTS; UNIFORM-CONVERGENCE; THEOREMS; INEQUALITIES; MODULI;

D O I：

10.4064/sm193-3-5

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study weighted L(p)-integrability (1 <= p < infinity) of trigonometric series. It is shown how the integrability of a function with weight x(-alpha) depends on some regularity conditions on Fourier coefficients. Criteria for the uniform convergence of trigonometric series in terms of their coefficients are also studied.

引用

页码：285 / 306

页数：22

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