Weighted Integrability of Multiplicative Fourier Transforms

被引：2

作者：

Volosivets, S. S. ^{[1
]}

Golubov, B. I. ^{[2
]}

机构：

[1] Saratov NG Chernyshevskii State Univ, Dept Mech & Math, Saratov 410012, Russia

[2] Moscow Inst Phys & Technol, Dolgoprudnyi 141700, Moscow Oblast, Russia

来源：

PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS | 2010年 / 269卷 / 01期

基金：

俄罗斯基础研究基金会;

关键词：

STEKLOV Institute; Hardy Inequality; Multiplicative FOURIER; Weighted Integrability; Fourier Integral;

D O I：

10.1134/S0081543810020069

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the relationship between the weighted integrability of a function and that of its multiplicative Fourier transform (MFT). In particular, for the MFT we prove an analog of R. Boas' conjecture related to the Fourier sine and cosine transforms. In addition, we obtain a sufficient condition under which a contraction of an MFT is also an MFT. For the moduli of continuity omega satisfying N.K. Bari's condition, we present a criterion for determining whether a function with a nonnegative MFT belongs to the class H(omega).

引用

页码：65 / 75

页数：11

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