Abstract
For a family of weight functionsh K invariant under a finite reflection group onR d, analysis related to the Dunkl transform is carried out for the weightedL 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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ST wishes to thank YX for the warm hospitality during his stay in Eugene. The work of YX was supported in part by the National Science Foundation under Grant DMS-0201669.
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Thangavelu, S., Xu, Y. Convolution operator and maximal function for the Dunkl transform. J. Anal. Math. 97, 25–55 (2005). https://doi.org/10.1007/BF02807401
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DOI: https://doi.org/10.1007/BF02807401