TY - JOUR
AU - Abdelkefi, Chokri
PY - 2020/03/03
Y2 - 2023/11/29
TI - Maximal functions for Weinstein operator
JF - Annales Universitatis Paedagogicae Cracoviensis Studia Mathematica
JA - Ann. Univ. Paedagog. Crac. Stud. Math.
VL - 19
IS -
SE - Published
DO -
UR - https://studmath.up.krakow.pl/article/view/7927
SP - 105-119
AB - <p>In the present paper, we study in the harmonic analysis associated to the Weinstein operator, the boundedness on <em>L<sup>p</sup></em> 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 <strong>R</strong><sup>d-1</sup>× ]0,+∞[. Second, we prove weak-type <em>L<sup>1</sup></em>-estimates for the uncentered maximal function associated with the Weinstein operator and we obtain the <em>L<sup>p</sup></em>-boundedness of this operator for 1 < <em>p</em> ≤+∞. As application, we define a large class of operators such that each operator of this class satisfies these <em>L<sup>p</sup></em>-inequalities. In particular, the maximal operator associated respectively with the Weinstein heat semigroup and the Weinstein-Poisson semigroup belong to this class.</p>
ER -