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Journal of Lie Theory 20 (2010), No. 1, 113--125
Copyright Heldermann Verlag 2010

Dunkl Operators on Rd and Uncentered Maximal Function

Chokri Abdelkefi
University of Tunis, Preparatory Institute of Engineering Studies, Department of Mathematics, 1089 Monfleury-Tunis, Tunisia

We consider Dunkl theory on Rd associated to a finite reflection group G. We establish first an estimate for the Dunkl translation of the characteristic function of a closed ball with radius ε > 0 centered at 0. Second, we prove that the uncentered maximal function associated with the Dunkl operators is of weak-type (1, 1). We finally obtain that it is strong-type (p, p) for 1 < p ≤ +∞.

Keywords: Dunkl operators, Dunkl transform, Dunkl translations, uncentered maximal function.

MSC: 42B10, 42B25, 44A15, 44A35

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