Article,
Bessel potentials, hitting distributions and Green functions
Trans. Amer. Math. Soc., 361 (9): 4871--4900 (2009)
DOI: 10.1090/S0002-9947-09-04657-1
Abstract
The purpose of the paper is to find explicit formulas for basic objects pertaining to the potential theory of the operator $ (I-\Delta)^\alpha/2$, which is based on Bessel potentials $ J_\alpha=(I-\Delta)^-\alpha/2$, $ 0<\alpha<2$. We compute the harmonic measure of the half-space and obtain a concise form for the corresponding Green function of the operator $ (I-\Delta)^\alpha/2$. As an application we provide sharp estimates for the Green function of the half-space for the relativistic process.
