# On the Green Function and Poisson Integrals of the Dunkl Laplacian

@article{Graczyk2016OnTG,
title={On the Green Function and Poisson Integrals of the Dunkl Laplacian},
author={Piotr Graczyk and Tomasz Luks and Margit R{\"o}sler},
journal={Potential Analysis},
year={2016},
volume={48},
pages={337-360}
}
• Published 2016
• Mathematics
• Potential Analysis
We prove the existence and study properties of the Green function of the unit ball for the Dunkl Laplacian △k in ℝd$\mathbb {R}^{d}$. 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 ℝd$\mathbb {R}^{d}$. These estimates contrast sharply with the well-known results in the potential… Expand
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