Methods and Applications of Analysis

Bessel and Flett Potentials associated with Dunkl Operators on $\Bbb R^d$

Néjib Ben Salem, Anis El Garna, and Samir Kallel

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Analogous of Bessel and Flett potentials are defined and studied for the Dunkl transform associated with a family of weighted functions that are invariant under a reflection group. We show that the Dunkl-Bessel potentials, of positive order, can be represented by an integral involving the k-heat transform and we give some applications of this result. Also, we obtain an explicit inversion formula for the Dunkl-Flett potentials, which are interpreted as negative fractional powers of a certain operator expressed in terms of the Dunkl-Laplacian.

Article information

Methods Appl. Anal., Volume 15, Number 4 (2008), 477-494.

First available in Project Euclid: 2 October 2009

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 32A55: Singular integrals 47H5O 31A1O

Dunkl operator Poisson transform heat transform Bessel potential Flett potential


Ben Salem, Néjib; El Garna, Anis; Kallel , Samir. Bessel and Flett Potentials associated with Dunkl Operators on $\Bbb R^d$. Methods Appl. Anal. 15 (2008), no. 4, 477--494.

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