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Riesz transforms for Dunkl transform

Bechir Amri; Mohamed Sifi — 2012

Annales mathématiques Blaise Pascal

In this paper we obtain the $L^{p}$ -boundedness of Riesz transforms for the Dunkl transform for all $1 < p < \infty$ .

Three results in Dunkl analysis

Béchir Amri; Jean-Philippe Anker; Mohamed Sifi — 2010

Colloquium Mathematicae

We first establish a geometric Paley-Wiener theorem for the Dunkl transform in the crystallographic case. Next we obtain an optimal bound for the $L^{p} \to L^{p}$ norm of Dunkl translations in dimension 1. Finally, we describe more precisely the support of the distribution associated to Dunkl translations in higher dimension.

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