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Boundary Harnack Principle and Martin Boundary at Infinity for Subordinate Brownian Motions |
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| Authors: | Panki Kim Renming Song Zoran Vondraček |
| Affiliation: | 1. Department of Mathematical Sciences and Research Institute of Mathematics, Seoul National University, Building 27, 1 Gwanak-ro, Gwanak-gu Seoul, 151-747, Republic of Korea 2. Department of Mathematics, University of Illinois, Urbana, IL, 61801, USA 3. Department of Mathematics, University of Zagreb, Zagreb, Croatia |
| Abstract: | In this paper we study the Martin boundary of unbounded open sets at infinity for a large class of subordinate Brownian motions. We first prove that, for such subordinate Brownian motions, the uniform boundary Harnack principle at infinity holds for arbitrary unbounded open sets. Then we introduce the notion of κ-fatness at infinity for open sets and show that the Martin boundary at infinity of any such open set consists of exactly one point and that point is a minimal Martin boundary point. |
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