A Hardy–Littlewood Maximal Operator for the Generalized Fourier Transform on R

Salem Ben Saïd, Luc Deleaval

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)

Abstract

In this paper, we define and study a canonical Hardy–Littlewood-type maximal operator associated with the one-dimensional generalized Fourier transform. For this operator to which covering methods do not apply, we construct a geometric maximal operator, which controls pointwise the canonical maximal operator, and for which we can use the machinery of real analysis to obtain a maximal theorem.

Original languageEnglish
Pages (from-to)2273-2289
Number of pages17
JournalJournal of Geometric Analysis
Volume30
Issue number2
DOIs
Publication statusPublished - Apr 1 2020

Keywords

  • Generalized Fourier transform
  • Hardy–Littlewood maximal theorem
  • Maximal function

ASJC Scopus subject areas

  • Geometry and Topology

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