Norm inequalities for maximal operators

Salem Ben Said; Selma Negzaoui

doi:10.1186/s13660-022-02874-1

Norm inequalities for maximal operators

Salem Ben Said, Selma Negzaoui

Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

7 Citations (Scopus)

Abstract

In this paper, we introduce a family of one-dimensional maximal operators M_κ_,_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 M_κ_,_m, p> 1. To do so, we prove a technical covering lemma for a finite collection of intervals.

Original language	English
Article number	134
Journal	Journal of Inequalities and Applications
Volume	2022
Issue number	1
DOIs	https://doi.org/10.1186/s13660-022-02874-1
Publication status	Published - 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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10.1186/s13660-022-02874-1

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AB - 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.

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KW - Generalized Fourier transform

KW - Maximal operators

KW - Weak and strong type inequalities

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ER -

Norm inequalities for maximal operators

Abstract

Keywords

ASJC Scopus subject areas

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