<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

Publicado en línea: 31 dic 2020

Páginas: 105 - 119

Recibido: 04 sept 2019

Aceptado: 22 nov 2019

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

Palabras clave
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

Publicado en línea: 31 dic 2020

Páginas: 105 - 119

Recibido: 04 sept 2019

Aceptado: 22 nov 2019

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

Palabras claveWeinstein 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.

Palabras clave
Weinstein operator, Weinstein transform, Weinstein translation operators, Maximal functions