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.

引用

页码：553 / 561

页数：9

共 14 条

[1]

[Anonymous], 2014, Operator Theory: Advances and Applications, DOI [DOI 10.1007/978-3-0348-0648-0_17, 10.1007/978-3-0348-0648-0_17]

[2]

Bennett C., 1988, INTERPOLATION OPERAT, V129

[3]

COIFMAN RR, 1974, STUD MATH, V51, P241

[4] Weighted norm inequalities for the maximal operator on variable Lebesgue spaces [J].