Riesz transforms for Dunkl transform

In this paper we obtain the $L^p$-boundedness of Riesz transforms for Dunkl transform for all $1<p<\infty$.Comment: 12 page

On the Uniform Convergence of Partial Dunkl Integrals in Besov-Dunkl Spaces

2000 Mathematics Subject Classification: 44A15, 44A35, 46E30In this paper we prove that the partial Dunkl integral ST(f) of f converges to f, as T → +∞ in L^∞(νµ) and we show that the Dunkl transform Fµ(f) of f is in L^1(νµ) when f belongs to a suitable Besov-Dunkl space. We also give sufficient conditions on a function f in order that the Dunkl transform Fµ(f) of f is in a L^p -space.* Supported by 04/UR/15-02

Discrete harmonic functions on an orthant in Zd

International audienceWe give a positive answer to a conjecture on the uniqueness of harmonic functions in the quarter plane stated by K. Raschel. More precisely we prove the existence and uniqueness of a positive discrete harmonic function for a random walk satisfying finite range, centering and ellipticity conditions, killed at the boundary of an orthant in Zd. Our methodsallow on the other hand to generalize from the quarter plane to orthants in higher dimensions and to treat the spatially inhomogeneous walks

Herz-Type Hardy Spaces for the Dunkl Operator on the Real Line

2000 Mathematics Subject Classification: Primary 46F12, Secondary 44A15, 44A35We introduce some new weighted Herz spaces associated with the Dunkl operator on R. Also we characterize by atomic decompositions the corresponding Herz-type Hardy spaces. As applications we investigate the Dunkl transform on these spaces and establish a version of Hardy inequality for this transform.* The authors are supported by the DGRST research project 04/UR/15-02

Commutants of the Dunkl Operators in C(R)

2000 Mathematics Subject Classification: 44A35; 42A75; 47A16, 47L10, 47L80The Dunkl operators.* Supported by the Tunisian Research Foundation under 04/UR/15-02