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 α ∈ (0,2]. This process has an infinitesimal generator of the form . As an application we prove the global scale invariant Harnack inequality as well as the boundary Harnack principle.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm129-1-2,
author = {Tomasz Grzywny and Micha\l\ Ryznar},
title = {Potential theory of one-dimensional geometric stable processes},
journal = {Colloquium Mathematicae},
volume = {126},
year = {2012},
pages = {7-40},
zbl = {1276.60083},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm129-1-2}
}
Tomasz Grzywny; Michał Ryznar. Potential theory of one-dimensional geometric stable processes. Colloquium Mathematicae, Tome 126 (2012) pp. 7-40. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm129-1-2/