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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.
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https://hal.archives-ouvertes.fr/hal-01358021
Contributor : Piotr Graczyk <>
Submitted on : Tuesday, August 30, 2016 - 6:17:51 PM
Last modification on : Monday, March 9, 2020 - 6:16:03 PM

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  • HAL Id : hal-01358021, version 1

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

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