NONCOMPACTNESS OF FOURIER CONVOLUTION OPERATORS ON BANACH FUNCTION SPACES

被引：5
|
作者：
Fernandes, Claudio A. [1 ]
Karlovich, Alexei Y. [1 ]
Karlovich, Yuri, I [2 ]
机构：
[1] Univ Nova Lisboa, Fac Ciencias & Tecnol, Dept Matemat, Ctr Matemat & Aplicacoes, P-2829516 Caparica, Portugal
[2] Univ Autonoma Estado Morelos, Inst Invest Ciencias Basicas & Aplicadas, Ctr Invest Ciencias, AV Univ 1001, Cuernavaca 62209, Morelos, Mexico
来源：
ANNALS OF FUNCTIONAL ANALYSIS | 2019年 / 10卷 / 04期
关键词：
Fourier convolution operator; compactness; Banach function space; Hardy-Littlewood maximal operator; Lebesgue space with Muckenhoupt weight; WEIGHTED NORM INEQUALITIES; MAXIMAL OPERATOR;
D O I：
10.1215/20088752-2019-0013
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Let X(R) be a separable Banach function space such that the Hardy-Littlewood maximal operator M is bounded on X(R) and on its associate space X' (R). Suppose that a is a Fourier multiplier on the space X(R) We show that the Fourier convolution operator W-0(a) with symbol a is compact on the space X(R) if and only if a = 0. This result implies that nontrivial Fourier convolution operators on Lebesgue spaces with Muckenhoupt weights are never compact.
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页码：553 / 561
页数：9
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