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Higher order Riesz transforms for the Dunkl Ornstein-Uhlenbeck operator

Walid Nefzi — 2019

Czechoslovak Mathematical Journal

The aim of this paper is to extend the study of Riesz transforms associated to Dunkl Ornstein-Uhlenbeck operator considered by A. Nowak, L. Roncal and K. Stempak to higher order.

Images of some functions and functional spaces under the Dunkl-Hermite semigroup

Néjib Ben Salem; Walid Nefzi — 2013

Commentationes Mathematicae Universitatis Carolinae

We propose the study of some questions related to the Dunkl-Hermite semigroup. Essentially, we characterize the images of the Dunkl-Hermite-Sobolev space, $𝒮 (ℝ)$ and $L_{α}^{p} (ℝ)$ , $1 < p < \infty$ , under the Dunkl-Hermite semigroup. Also, we consider the image of the space of tempered distributions and we give Paley-Wiener type theorems for the transforms given by the Dunkl-Hermite semigroup.

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