Bessel potentials, hitting distributions and Green functions

Byczkowski, T.; Małecki, J.; Ryznar, M.

doi:10.1090/S0002-9947-09-04657-1

Bessel potentials, hitting distributions and Green functions
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by T. Byczkowski, J. Małecki and M. Ryznar PDF

Trans. Amer. Math. Soc. 361 (2009), 4871-4900 Request permission

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.

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