Translation operator and maximal function for the (k,1)-generalized Fourier transform

Salem Ben Saïd, Luc Deleaval

Research output: Contribution to journalArticlepeer-review

15 Citations (Scopus)

Abstract

In this paper we study a translation operator associated with the n-dimensional (k,1)-generalized Fourier transform, where k is a multiplicity function for the Dunkl operators. In particular, we prove that the translation is a positivity-preserving operator acting on a suitable space of radial functions on Rn. We then use it to define a Hardy-Littlewood type maximal operator, where weak-type (1,1) and strong-type (p,p) estimates for the maximal operator are established with a precise behavior in n and k.

Original languageEnglish
Article number108706
JournalJournal of Functional Analysis
Volume279
Issue number8
DOIs
Publication statusPublished - Nov 1 2020

Keywords

  • Dunkl's intertwining operator
  • Generalized Fourier transform
  • Generalized translation operator
  • Hardy-Littlewood type maximal operator

ASJC Scopus subject areas

  • Analysis

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