Norm inequalities for maximal operators

Salem Ben Said, Selma Negzaoui

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)

Abstract

In this paper, we introduce a family of one-dimensional maximal operators Mκ,m, κ≥ 0 and m∈ N∖ { 0 } , which includes the Hardy–Littlewood maximal operator as a special case (κ= 0 , m= 1). We establish the weak type (1 , 1) and the strong type (p, p) inequalities for Mκ,m, p> 1. To do so, we prove a technical covering lemma for a finite collection of intervals.

Original languageEnglish
Article number134
JournalJournal of Inequalities and Applications
Volume2022
Issue number1
DOIs
Publication statusPublished - 2022

Keywords

  • Covering lemma
  • Generalized Fourier transform
  • Maximal operators
  • Weak and strong type inequalities

ASJC Scopus subject areas

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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