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Convolution operator and maximal function for the Dunkl transform
- Source :
- Journal d'Analyse Mathématique. 97:25-55
- Publication Year :
- 2005
- Publisher :
- Springer Science and Business Media LLC, 2005.
-
Abstract
- For a family of weight functions $h_k$ invariant under a finite reflection group on $R^d$, 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.
Details
- ISSN :
- 15658538 and 00217670
- Volume :
- 97
- Database :
- OpenAIRE
- Journal :
- Journal d'Analyse Mathématique
- Accession number :
- edsair.doi.dedup.....fb269e4b860bc132c8543b928939e829