ON THE GREEN FUNCTION AND POISSON INTEGRALS OF THE DUNKL LAPLACIAN
Résumé
We prove the existence and study properties of the Green function of the unit ball for the Dunkl Laplacian ∆ k in R d. As applications we derive the Poisson-Jensen formula for ∆ k-subharmonic functions and Hardy-Stein identities for the Poisson integrals of ∆ k. We also obtain sharp estimates of the Newton potential kernel, Green function and Poisson kernel in the rank one case in R d. These estimates contrast sharply with the well-known results in the potential theory of the classical Laplacian.
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