Algebras of Continuous Fourier Multipliers on Variable Lebesgue Spaces

被引：3

作者：

Karlovich, Alexei Yu. ^{[1
]}

机构：

[1] Univ Nova Lisboa, Dept Matemat, Ctr Matemat & Aplicacoes, Fac Ciencias & Tecnol, P-2829516 Caparica, Portugal

来源：

MEDITERRANEAN JOURNAL OF MATHEMATICS | 2020年 / 17卷 / 04期

关键词：

Continuous Fourier multiplier; variable Lebesgue space; Stechkin's inequality; piecewise continuous function; slowly oscillating function; 42B15; 46E30; CONVOLUTION TYPE OPERATORS; MAXIMAL-FUNCTION; SYMBOLS;

D O I：

10.1007/s00009-020-01537-z

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We show that several definitions of algebras of continuous Fourier multipliers on variable Lebesgue spaces over the real line are equivalent under some natural assumptions on variable exponents. Some of our results are new even in the case of standard Lebesgue spaces and give answers on two questions about algebras of continuous Fourier multipliers on Lebesgue spaces over the real line posed by Mascarenhas, Santos and Seidel.

引用

页数：19

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