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.
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页码：533 / 546
页数：14
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