On the Lebesgue summability of double trigonometric series

被引：2

作者：

Bagota, Monika ^{[2
]}

Moricz, Ferenc ^{[1
]}

机构：

[1] Univ Szeged, Bolyai Inst, H-6720 Szeged, Hungary

[2] Univ Szeged, Teachers Training Coll, H-6725 Szeged, Hungary

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2008年 / 348卷 / 01期

关键词：

formal integration of double trigonometric series; symmetric derivative and its extension to functions in two variables; the Lebesgue method of summability;

D O I：

10.1016/j.jmaa.2008.07.064

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We recall that the Lebesgue summability of a single trigonometric series is defined in terms of the symmetric differentiability of the sum of the formally integrated trigonometric series in question. In this paper, we present another proof of the theorem given in Zygmund's monograph. Then we define the notion of Lebesgue summability of a double trigonometric series and extend the theorem of Fatou and Zygmund from single to double trigonometric series. (C) 2008 Published by Elsevier Inc.

引用

页码：555 / 561

页数：7

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