Fourier Series in Weighted Lorentz Spaces

被引：2
|
作者：
Rastegari, Javad [1 ]
Sinnamon, Gord [1 ]
机构：
[1] Univ Western Ontario, Dept Math, London, ON, Canada
来源：
JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS | 2016年 / 22卷 / 05期
基金：
加拿大自然科学与工程研究理事会;
关键词：
Fourier series; Fourier coefficients; Weights; Lorentz space; LAPLACE TRANSFORM; HARDY-SPACES; INEQUALITIES;
D O I：
10.1007/s00041-015-9455-5
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The Fourier coefficient map is considered as an operator from a weighted Lorentz space on the circle to a weighted Lorentz sequence space. For a large range of Lorentz indices, necessary and sufficient conditions on the weights are given for the map to be bounded. In addition, new direct analogues are given for known weighted Lorentz space inequalities for the Fourier transform. Applications are given that involve Fourier coefficients of functions in LogL and more general Lorentz-Zygmund spaces.
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页码：1192 / 1223
页数：32
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