ON THE INTEGRABILITY AND UNIFORM CONVERGENCE OF MULTIPLICATIVE FOURIER TRANSFORMS

被引：0

作者：

Golubov, Boris I. ^{[1
]}

Volosivets, Sergey S. ^{[2
]}

机构：

[1] State Univ, Moscow Inst Phys & Technol, Dolgoprudnyi 141700, Moscow Region, Russia

[2] Saratov NG Chernyshevskii State Univ, Dept Mech & Math, Saratov 410028, Russia

来源：

GEORGIAN MATHEMATICAL JOURNAL | 2009年 / 16卷 / 03期

基金：

俄罗斯基础研究基金会;

关键词：

Multiplicative Fourier transform; integrability; uniform convergence; Nikol'skii type inequality; SERIES;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Analogues of two Hardy-Littlewood theorems are proved for a multiplicative Fourier transform. A Szasz type condition for a multiplicative Fourier transform is given and its nonimprovability is proved. Besides, an analogue of Ul'yanov's theorem on the uniform convergence of a trigonometric series and an analogue of Konyuskov-Stechkin's embedding theorem are obtained by means of a Nikol'skii type inequality of various metrics.

引用

页码：533 / 546

页数：14

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