Algebras of Continuous Fourier Multipliers on Variable Lebesgue Spaces
Classical Analysis and ODEs
2019-03-26 v1 Functional Analysis
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 H. Mascarenhas, P. Santos and M. Seidel.
Keywords
Cite
@article{arxiv.1903.09696,
title = {Algebras of Continuous Fourier Multipliers on Variable Lebesgue Spaces},
author = {Alexei Karlovich},
journal= {arXiv preprint arXiv:1903.09696},
year = {2019}
}
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19 pages