Convergence of trigonometric series with general monotone coefficients

被引：26
|
作者：
Dyachenko, Mikhail [1 ]
Tikhonov, Sergey
机构：
[1] Moscow MV Lomonosov State Univ, Moscow 117234, Russia
[2] Scuola Normale Super Pisa, I-56126 Pisa, Italy
来源：
COMPTES RENDUS MATHEMATIQUE | 2007年 / 345卷 / 03期
关键词：
D O I：
10.1016/j.crma.2007.06.009
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this Note we study the convergence results for trigonometric series in L-p-spaces on one-dimensional and n-dimension torus. The sufficient conditions for these results to hold as well as criteria are written for the series with general monotone coefficients. The Hardy-Littlewood type theorem is obtained for multiple series. Several corollaries, in particular, u-convergence are presented.
引用
收藏
页码：123 / 126
页数：4
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