Convolution operator and maximal function for Dunkl transform

Details Convolution operator and maximal function for Dunkl transform Convolution operator and maximal function for Dunkl transform

2004-03-02

arxiv.org/abs/math/0403049v4

Mathematics

Classical Analysis and ODEs

25 pages, accepted for publication by J. d'Analyse Mathematique

Scientific paper

For a family of weight functions, $h_\kappa$, invariant under a finite reflection group on $\RR^d$, analysis related to the Dunkl transform is carried out for the weighted $L^p$ spaces. Making use of the generalized translation operator and the weighted convolution, we study the summability of the inverse Dunkl transform, including as examples the Poisson integrals and the Bochner-Riesz means. We also define a maximal function and use it to prove the almost everywhere convergence.

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