On a class of summability methods for multiple Fourier series

被引：5
|
作者：
Dyachenko, M. I. [1 ]
机构：
[1] Moscow MV Lomonosov State Univ, Fac Mech & Math, Moscow, Russia
来源：
SBORNIK MATHEMATICS | 2013年 / 204卷 / 03期
基金：
俄罗斯基础研究基金会;
关键词：
multiple Fourier series; summability methods; generalized Cesaro means;
D O I：
10.1070/SM2013v204n03ABEH004302
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The paper shows that the same properties which hold for the classical (C, 1)-means are preserved for a sufficiently large class of summability methods for multiple Fourier series involving rectangular partial sums. More precisely, Fourier series of continuous functions are uniformly summable by these methods, and Fourier series of functions from the class L(ln + L)(m-1) (T-m) are summable almost everywhere.
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页码：307 / 322
页数：16
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