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Estimates and structure of $\alpha$-harmonic functions

Krzysztof Bogdan·Tadeusz Kulczycki·Mateusz Kwaśnicki
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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.

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Krzysztof Bogdan, Tadeusz Kulczycki, Mateusz Kwaśnicki. 2006-07-22. Estimates and structure of $\alpha$-harmonic functions. https://doi.org/10.1007/s00440-007-0067-0

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