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Estimates and structure of α-harmonic functions |
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| Authors: | Krzysztof Bogdan Tadeusz Kulczycki Mateusz Kwaśnicki |
| Institution: | (1) Department of Statistics, Purdue University, West Lafayette, IN 47906, USA;(2) Institute of Mathematics and Computer Science, Wrocław University of Technology, ul. Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland |
| 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 ∪ {∞} satisfying an integrability condition. The corresponding Martin boundary of D is a subset of the Euclidean boundary determined by an integral test. K. Bogdan was supported by KBN grant 1 P03A 026 29 and RTN contract HPRN-CT-2001-00273-HARP. T. Kulczycki was supported by KBN grant 1 P03A 020 28 and RTN contract HPRN-CT-2001-00273-HARP. M. Kwaśnicki was supported by KBN grant 1 P03A 020 28 and RTN contractHPRN-CT-2001-00273-HARP. |
| Keywords: | Boundary Harnack inequality Martin representation Stable process |
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