INVERTIBILITY OF FOURIER CONVOLUTION OPERATORS WITH PIECEWISE CONTINUOUS SYMBOLS ON BANACH FUNCTION SPACES

被引：0

作者：

Fernandes, Claudio ^{[1
,2
]}

Karlovich, Alexei ^{[1
,2
]}

Valente, Marcio ^{[2
]}

机构：

[1] Univ Nova Lisboa, Fac Ciencias & Tecnol, Ctr Matemat & Aplicaoes CMA, P-2829516 Quinta Da Torre, Caparica, Portugal

[2] Univ Nova Lisboa, Fac Ciencias & Tecnol, Dept Matemat, P-2829516 Quinta Da Torre, Caparica, Portugal

来源：

TRANSACTIONS OF A RAZMADZE MATHEMATICAL INSTITUTE | 2021年 / 175卷 / 01期

关键词：

Fourier convolution operator; Fourier multiplier; Piecwise constant function; Piecewise continuous function; Invertibility;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We extend results on the invertibility of Fourier convolution operators with piecewise continuous symbols on the Lebesgue space L-p (R), p is an element of (1, infinity), obtained by Roland Duduchava in the late 1970s, to the setting of a separable Banach function space X(R) such that the Hardy-Littlewood maximal operator is bounded on X(R) and on its associate space X'(R). We specify our results in the case of rearrangement-invariant spaces with suitable Muckenhoupt weights.

引用

页码：49 / 61

页数：13

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