Maximal functions for Weinstein operator
Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica, Tome 19 (2020), pp. 105-119.

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In the present paper, we study in the harmonic analysis associated to the Weinstein operator, the boundedness on L^p of the uncentered maximal function. First, we establish estimates for the Weinstein translation of characteristic function of a closed ball with radius ε centered at 0 on the upper half space ^d-1× ]0,+∞[. Second, we prove weak-type L^1-estimates for the uncentered maximal function associated with the Weinstein operator and we obtain the L^p-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 L^p-inequalities. In particular, the maximal operator associated respectively with the Weinstein heat semigroup and the Weinstein-Poisson semigroup belong to this class.
Keywords: Weinstein operator, Weinstein transform, Weinstein translation operators, Maximal functions
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Abdelkefi, Chokri. Maximal functions for Weinstein operator. Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica, Tome 19 (2020), pp. 105-119. http://geodesic.mathdoc.fr/item/AUPCM_2020_19_a8/

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