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arXiv · 1107.0745

Potential theory of one-dimensional geometric stable processes

Tomasz Grzywny·Michał Ryznar
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Abstract

The purpose of this paper is to find optimal estimates for the Green function and the Poisson kernel for a half-line and intervals of the geometric stable process with parameter $\alpha\in(0,2]$. This process has an infinitesimal generator of the form $-\log(1+(-\Delta)^{\alpha/2})$. As an application we prove the scale invariant Harnack inequality as well as the boundary Harnack principle.

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Tomasz Grzywny, Michał Ryznar. 2011-07-04. Potential theory of one-dimensional geometric stable processes. https://arxiv.org/abs/1107.0745

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