Algebras of Continuous Fourier Multipliers on Variable Lebesgue Spaces

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Abstract

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.

Original languageEnglish
Article number102
JournalMediterranean Journal of Mathematics
Volume17
Issue number4
DOIs
Publication statusPublished - 1 Aug 2020

Keywords

  • Continuous Fourier multiplier
  • piecewise continuous function
  • slowly oscillating function
  • Stechkin’s inequality
  • variable Lebesgue space

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