<abstract xmlns="http://www.w3.org/1999/xhtml">In the present paper, we study in the harmonic analysis associated to the Weinstein operator, the boundedness on <italic>L</italic><italic>p</italic> of the uncentered maximal function. First, we establish estimates for the Weinstein translation of characteristic function of a closed ball with radius <italic>ɛ</italic> centered at 0 on the upper half space ℝd–1× ]0, +∞ [. Second, we prove weak-type <italic>L</italic>1-estimates for the uncentered maximal function associated with the Weinstein operator and we obtain the <italic>L</italic><italic>p</italic>-boundedness of this operator for 1 &lt; <italic>p</italic> ≤ + ∞. As application, we define a large class of operators such that each operator of this class satisfies these <italic>L</italic><italic>p</italic>-inequalities. In particular, the maximal operator associated respectively with the Weinstein heat semigroup and the Weinstein-Poisson semigroup belong to this class.</abstract>

In the present paper, we study in the harmonic analysis associated to the Weinstein operator, the boundedness on Lp of the uncentered maximal function. First, we establish estimates for the Weinstein translation of characteristic function of a closed ball with radius ɛ centered at 0 on the upper half space ℝd–1× ]0, +∞ [. Second, we prove weak-type L1-estimates for the uncentered maximal function associated with the Weinstein operator and we obtain the Lp-boundedness of this operator for 1 < p ≤ + ∞. As application, we define a large class of operators such that each operator of this class satisfies these Lp-inequalities. In particular, the maximal operator associated respectively with the Weinstein heat semigroup and the Weinstein-Poisson semigroup belong to this class.

Maximal functions for Weinstein operator

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

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{"article-title":"Maximal functions for Weinstein operator"}

In the present paper, we study in the harmonic analysis associated to the Weinstein operator, the boundedness on Lp of the uncentered maximal function. First,...

Maximal functions for Weinstein operator

Published Online: Dec 31, 2020

Page range: 105 - 119

Received: Sep 04, 2019

Accepted: Nov 22, 2019

DOI: https://doi.org/10.2478/aupcsm-2020-0009

Keywords
Weinstein operator, Weinstein transform, Weinstein translation operators, Maximal functions

© 2020 Chokri Abdelkefi, published by Sciendo

This work is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.

Maximal functions for Weinstein operator

Published Online: Dec 31, 2020

Page range: 105 - 119

Received: Sep 04, 2019

Accepted: Nov 22, 2019

DOI: https://doi.org/10.2478/aupcsm-2020-0009

KeywordsWeinstein operator, Weinstein transform, Weinstein translation operators, Maximal functions

© 2020 Chokri Abdelkefi, published by Sciendo

This work is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.

Keywords
Weinstein operator, Weinstein transform, Weinstein translation operators, Maximal functions