Boundary potential theory for stable Lévy processes

Paweł Sztonyk. "Boundary potential theory for stable Lévy processes." Colloquium Mathematicae 95.2 (2003): 191-206. <http://eudml.org/doc/285228>.

@article{PawełSztonyk2003,
abstract = {We investigate properties of harmonic functions of the symmetric stable Lévy process on $ℝ^\{d\}$ without the assumption that the process is rotation invariant. Our main goal is to prove the boundary Harnack principle for Lipschitz domains. To this end we improve the estimates for the Poisson kernel obtained in a previous work. We also investigate properties of harmonic functions of Feynman-Kac semigroups based on the stable process. In particular, we prove the continuity and the Harnack inequality for such functions.},
author = {Paweł Sztonyk},
journal = {Colloquium Mathematicae},
keywords = {boundary Harnack principle; stable process; -harmonic function; Carleson estimate},
language = {eng},
number = {2},
pages = {191-206},
title = {Boundary potential theory for stable Lévy processes},
url = {http://eudml.org/doc/285228},
volume = {95},
year = {2003},
}

TY - JOUR
AU - Paweł Sztonyk
TI - Boundary potential theory for stable Lévy processes
JO - Colloquium Mathematicae
PY - 2003
VL - 95
IS - 2
SP - 191
EP - 206
AB - We investigate properties of harmonic functions of the symmetric stable Lévy process on $ℝ^{d}$ without the assumption that the process is rotation invariant. Our main goal is to prove the boundary Harnack principle for Lipschitz domains. To this end we improve the estimates for the Poisson kernel obtained in a previous work. We also investigate properties of harmonic functions of Feynman-Kac semigroups based on the stable process. In particular, we prove the continuity and the Harnack inequality for such functions.
LA - eng
KW - boundary Harnack principle; stable process; -harmonic function; Carleson estimate
UR - http://eudml.org/doc/285228
ER -