On the absolute convergence of multiple fourier series

被引：10

作者：

Moricz, Ferenc ^{[1
]}

Veres, Antal ^{[1
]}

机构：

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

来源：

ACTA MATHEMATICA HUNGARICA | 2007年 / 117卷 / 03期

关键词：

multiple Fourier series; absolute convergence; multiplicative moduli of continuity; functions of bounded variation in the sense of Vitali and of Hardy and Krause; absolutely continuous functions of several variables; multivariate versions of Bernstein's theorem and Zygmund's theorem;

D O I：

10.1007/s10474-007-6100-z

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let f : R-N C be a periodic function with period 2 pi in each variable. We prove sufficient conditions for the absolute convergence of the multiple Fourier series of f in terms of moduli of continuity, of bounded variation in the sense of Vitali or Hardy and Krause, and of the mixed partial derivative ill case f is an absolutely continuous function. Our results extend the classical theorems of Bernstein and Zygmund from single to multiple Fourier series.

引用

页码：275 / 292

页数：18

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