Estimates and structure of $\alpha$-harmonic functions
Probability
2017-02-15 v2
Abstract
We prove a uniform boundary Harnack inequality for nonnegative harmonic functions of the fractional Laplacian on arbitrary open set . This yields a unique representation of such functions as integrals against measures on satisfying an integrability condition. The corresponding Martin boundary of is a subset of the Euclidean boundary determined by an integral test.
Cite
@article{arxiv.math/0607561,
title = {Estimates and structure of $\alpha$-harmonic functions},
author = {Krzysztof Bogdan and Tadeusz Kulczycki and Mateusz Kwaśnicki},
journal= {arXiv preprint arXiv:math/0607561},
year = {2017}
}
Comments
32 pages The original publication in Probability Theory and Related Fields available at www.springerlink.com