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Convolution operator and maximal function for the Dunkl transform

Thangavelu, Sundaram and Xu, Yuan (2005) Convolution operator and maximal function for the Dunkl transform. In: Journal d'Analyse Mathématique, 97 (1). pp. 25-55.

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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.

Item Type: Journal Article
Additional Information: Copyright of this article belongs to Springer.
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Date Deposited: 24 Jul 2008
Last Modified: 27 Aug 2008 13:38
URI: http://eprints.iisc.ernet.in/id/eprint/15221

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