ON THE GREEN FUNCTION AND POISSON INTEGRALS OF THE DUNKL LAPLACIAN - Archive ouverte HAL Access content directly
Preprints, Working Papers, ... Year : 2016

ON THE GREEN FUNCTION AND POISSON INTEGRALS OF THE DUNKL LAPLACIAN

Abstract

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.
Fichier principal
Vignette du fichier
Dunkl_Green_SUBMITTED.pdf (342.67 Ko) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

Dates and versions

hal-01358021 , version 1 (30-08-2016)

Identifiers

  • HAL Id : hal-01358021 , version 1

Cite

Piotr Graczyk, Tomasz Luks, Margit Roesler. ON THE GREEN FUNCTION AND POISSON INTEGRALS OF THE DUNKL LAPLACIAN. 2016. ⟨hal-01358021⟩
111 View
214 Download

Share

Gmail Facebook X LinkedIn More