## Methods and Applications of Analysis

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

#### Abstract

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

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

Dates
First available in Project Euclid: 2 October 2009

https://projecteuclid.org/euclid.maa/1254492830

Mathematical Reviews number (MathSciNet)
MR2550074

Zentralblatt MATH identifier
1221.31009

Subjects
Primary: 32A55: Singular integrals 47H5O 31A1O

#### Citation

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. https://projecteuclid.org/euclid.maa/1254492830