Fourier Convolution Operators with Symbols Equivalent to Zero at Infinity on Banach Function Spaces

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Abstract

We study Fourier convolution operators W0(a) with symbols equivalent to zero at infinity on 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 show that the limit operators of W0(a) are all equal to zero.

Original languageEnglish
Title of host publicationCurrent Trends in Analysis, its Applications and Computation
Subtitle of host publicationProceedings of the 12th ISAAC Congress, Aveiro, Portugal, 2019
EditorsPaula Cerejeiras, Michael Reissig, Irene Sabadini, Joachim Toft
Place of PublicationCham
PublisherSpringer
Pages335-343
Number of pages9
ISBN (Electronic)978-3-030-87502-2
ISBN (Print)978-3-030-87501-5
DOIs
Publication statusPublished - 2022

Publication series

NameTrends in Mathematics
PublisherSpringer
ISSN (Print)2297-0215
ISSN (Electronic)2297-024X

Keywords

  • Banach function space
  • Equivalence at infinity
  • Fourier convolution operator
  • Fourier multiplier
  • Hardy-Littlewood maximal operator
  • Limit operator

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