Estimates and structure of $\alpha$-harmonic functions

Abstract

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.

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

References in corpus (1)

• Estimates of potential kernel and Harnack's inequality for anisotropic fractional Laplacian

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