On Dilations of Fourier Multipliers on Weighted Lebesgue Spaces

Oleksiy Karlovych, Eugene Shargorodsky

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

Abstract

For a given p∈(1,∞), we present an example of a Muckenhoupt weight w∈Ap and a Fourier multiplier a on the weighted Lebesgue space Lp(w) such that, for any τ∈ℝ∖{0,1}, the dilation of a given by aτ(ξ)=a(τξ) is not a Fourier multiplier on Lp(w).
Original languageEnglish
Title of host publicationAnalysis without Borders
Subtitle of host publicationDedicated to Ilya Spitkovsky on Occasion of his 70th Anniversary
EditorsSergei Rogosin
Place of PublicationCham
PublisherSpringer
Pages109-122
Number of pages14
ISBN (Electronic)978-3-031-59397-0
ISBN (Print)978-3-031-59396-3
DOIs
Publication statusPublished - Jul 2024

Publication series

NameOperator Theory: Advances and Applications
PublisherSpringer
Volume297
ISSN (Print)0255-0156
ISSN (Electronic)2296-4878

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