On harmonic functions of symmetric Levy processes
Probability
2012-01-25 v2
Abstract
We consider some classes of Levy processes for which the estimate of Krylov and Safonov (as in [BL02]) fails and thus it is not possible to use the standard iteration technique to obtain a-priori Holder continuity estimates of harmonic functions. Despite the faliure of this method, we obtain some a-priori regularity estimates of harmonic functions for these processes. Moreover, we extend results from [SSV06] and obtain asymptotic behavior of the Green function and the Levy density for a large class of subordinate Brownian motions, where the Laplace exponent of the corresponding subordinator is a slowly varying function.
Keywords
Cite
@article{arxiv.1109.3676,
title = {On harmonic functions of symmetric Levy processes},
author = {Ante Mimica},
journal= {arXiv preprint arXiv:1109.3676},
year = {2012}
}