Estimates and structure of $α$-harmonic functions

Details Estimates and structure of $α$-harmonic functions Estimates and structure of $α$-harmonic functions

2006-07-22

arxiv.org/abs/math/0607561v2

Mathematics

Probability

32 pages The original publication in Probability Theory and Related Fields available at www.springerlink.com

Scientific paper

10.1007/s00440-007-0067-0

We prove a uniform boundary Harnack inequality for nonnegative harmonic functions of the fractional Laplacian on arbitrary open set $D$. This yields a unique representation of such functions as integrals against measures on $D^c\cup \{\infty\}$ satisfying an integrability condition. The corresponding Martin boundary of $D$ is a subset of the Euclidean boundary determined by an integral test.

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