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Boundary Harnack Principle and Martin Boundary at Infinity for Subordinate Brownian Motions

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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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Authors and Affiliations

  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

    Panki Kim

  2. Department of Mathematics, University of Illinois, Urbana, IL, 61801, USA

    Renming Song

  3. Department of Mathematics, University of Zagreb, Zagreb, Croatia

    Zoran Vondraček

Authors
  1. Panki Kim
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  2. Renming Song
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  3. Zoran Vondraček
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Corresponding author

Correspondence to Zoran Vondraček.

Additional information

P. Kim was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government(MEST) (2013004822).

R. Song was supported in part by a grant from the Simons Foundation (208236).

Z. Vondraček was supported in part by the MZOS grant 037-0372790-2801.

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Kim, P., Song, R. & Vondraček, Z. Boundary Harnack Principle and Martin Boundary at Infinity for Subordinate Brownian Motions. Potential Anal 41, 407–441 (2014). https://doi.org/10.1007/s11118-013-9375-4

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  • DOI: https://doi.org/10.1007/s11118-013-9375-4

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