Let D be an open set in ℝⁿ (n ≥ 2) and ω(·,D) be the harmonic measure on with respect to the symmetric α-stable process (0 < α < 2) killed upon leaving D. We study inequalities on volumes or capacities which imply that a set S on ∂D has zero harmonic measure and others which imply that S has positive harmonic measure. In general, it is the relative sizes of the sets S and that determine whether ω(S,D) is zero or positive.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm149-3-5,
author = {Jang-Mei Wu},
title = {Harmonic measures for symmetric stable processes},
journal = {Studia Mathematica},
volume = {151},
year = {2002},
pages = {279-291},
zbl = {0990.60074},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm149-3-5}
}
Jang-Mei Wu. Harmonic measures for symmetric stable processes. Studia Mathematica, Tome 151 (2002) pp. 279-291. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm149-3-5/