Potential theory of one-dimensional geometric stable processes
Volume 129 / 2012
Colloquium Mathematicum 129 (2012), 7-40
MSC: Primary 60J45.
DOI: 10.4064/cm129-1-2
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 $-\log(1+(-{\mit\Delta})^{\alpha/2})$. As an application we prove the global scale invariant Harnack inequality as well as the boundary Harnack principle.
