Maximal functions for Weinstein operator

• Main Author: Chokri Abdelkefi
• Format: Article
• Language: deu
• Published: Wydawnictwo Naukowe Uniwersytetu Pedagogicznego 2020-03-01
• Series: Annales Universitatis Paedagogicae Cracoviensis: Studia Mathematica
• Subjects: weinstein operator; weinstein transform; weinstein translation operators; maximal functions
• Online Access: https://studmath.up.krakow.pl/index.php/studmath/article/view/7927

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 ε 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.