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 language | English |
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Article number | 134 |
Journal | Journal of Inequalities and Applications |
Volume | 2022 |
Issue number | 1 |
DOIs | |
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