Weighted Fourier Inequalities in Lebesgue and Lorentz Spaces

被引：4
|
作者：
Nursultanov, Erlan [1 ,2 ]
Tikhonov, Sergey [3 ,4 ,5 ]
机构：
[1] Gumilyov Eurasian Natl Univ, Kazakh Branch, Lomonosov Moscow State Univ, Munatpasova 7, Astana 010010, Kazakhstan
[2] Inst Math & Math Modelling, Alma Ata 050010, Kazakhstan
[3] Ctr Recerca Matemat, Campus Bellaterra,Edif C, Bellaterra 08193, Barcelona, Spain
[4] ICREA, Pg Lluis Companys 23, Barcelona 08010, Spain
[5] Univ Autonoma Barcelona, Barcelona, Spain
来源：
JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS | 2020年 / 26卷 / 04期
关键词：
Fourier transforms; Weights; Lebesgue and Lorentz spaces; Integral operators; Rearrangements; Hardy inequalities; Hormander-type conditions; NORM INEQUALITIES; TRANSFORM; OPERATORS; REARRANGEMENT; THEOREMS;
D O I：
10.1007/s00041-020-09764-4
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we obtain sufficient conditions for the weighted Fourier-type transforms to be bounded in Lebesgue and Lorentz spaces. Two types of results are discussed. First, we review the method based on rearrangement inequalities and the corresponding Hardy's inequalities. Second, we present Hormander-type conditions on weights so that Fourier-type integral operators are bounded in Lebesgue and Lorentz spaces. Both restricted weak- and strong-type results are obtained. In the case of regular weights necessary and sufficient conditions are given.
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页数：29
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