ar X iv : m at h / 04 03 04 9 v 3 [ m at h . C A ] 3 N ov 2 00 4 CONVOLUTION OPERATOR AND MAXIMAL FUNCTION FOR DUNKL TRANSFORM
نویسنده
چکیده
For a family of weight functions, hκ, invariant under a finite reflection group on R, analysis related to the Dunkl transform is carried out for the weighted L 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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ar X iv : m at h / 04 03 04 9 v 4 [ m at h . C A ] 2 9 Ju n 20 05 CONVOLUTION OPERATOR AND MAXIMAL FUNCTION FOR DUNKL TRANSFORM
For a family of weight functions, hκ, invariant under a finite reflection group on R, analysis related to the Dunkl transform is carried out for the weighted L 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 m...
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