Harnack inequality for stable processes on d-sets

Krzysztof Bogdan, Andrzej Stós, and Paweł Sztonyk. "Harnack inequality for stable processes on d-sets." Studia Mathematica 158.2 (2003): 163-198. <http://eudml.org/doc/285023>.

@article{KrzysztofBogdan2003,
abstract = {We investigate properties of functions which are harmonic with respect to α-stable processes on d-sets such as the Sierpiński gasket or carpet. We prove the Harnack inequality for such functions. For every process we estimate its transition density and harmonic measure of the ball. We prove continuity of the density of the harmonic measure. We also give some results on the decay rate of harmonic functions on regular subsets of the d-set. In the case of the Sierpiński gasket we even obtain the Boundary Harnack Principle.},
author = {Krzysztof Bogdan, Andrzej Stós, Paweł Sztonyk},
journal = {Studia Mathematica},
keywords = {stable processes; diffusions on fractals; Harnack inequality},
language = {eng},
number = {2},
pages = {163-198},
title = {Harnack inequality for stable processes on d-sets},
url = {http://eudml.org/doc/285023},
volume = {158},
year = {2003},
}

TY - JOUR
AU - Krzysztof Bogdan
AU - Andrzej Stós
AU - Paweł Sztonyk
TI - Harnack inequality for stable processes on d-sets
JO - Studia Mathematica
PY - 2003
VL - 158
IS - 2
SP - 163
EP - 198
AB - We investigate properties of functions which are harmonic with respect to α-stable processes on d-sets such as the Sierpiński gasket or carpet. We prove the Harnack inequality for such functions. For every process we estimate its transition density and harmonic measure of the ball. We prove continuity of the density of the harmonic measure. We also give some results on the decay rate of harmonic functions on regular subsets of the d-set. In the case of the Sierpiński gasket we even obtain the Boundary Harnack Principle.
LA - eng
KW - stable processes; diffusions on fractals; Harnack inequality
UR - http://eudml.org/doc/285023
ER -