On Convergence Properties of Tensor Products of Some Operator Sequences

被引：6

作者：

Gat, Gyorgy ^{[1
]}

Karagulyan, Grigori ^{[2
]}

机构：

[1] Univ Debrecen, Inst Math, Pf 12, H-4010 Debrecen, Hungary

[2] Armenian Natl Acad Sci, Inst Math, Baghramyan Ave 24-5, Yerevan 0019, Armenia

来源：

JOURNAL OF GEOMETRIC ANALYSIS | 2016年 / 26卷 / 04期

关键词：

Almost everywhere summability; Multiple Fourier series; Operators in functional spaces; CESARO SUMMABILITY; RESPECT; SERIES;

D O I：

10.1007/s12220-015-9662-y

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider sequences of compact bounded linear operators with certain convergence properties. Several divergence theorems for multiple sequences of tensor products of these operators are proved. These theorems in particular imply that is the optimal Orlicz space guaranteeing almost everywhere summability of rectangular partial sums of multiple Fourier series in general orthogonal systems.

引用

页码：3066 / 3089

页数：24

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