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

被引：8

作者：

Kim, Panki ^{[1
,2
]}

Song, Renming ^{[3
]}

Vondracek, Zoran ^{[4
]}

机构：

[1] Seoul Natl Univ, Dept Math Sci, Seoul 151747, South Korea

[2] Seoul Natl Univ, Res Inst Math, Seoul 151747, South Korea

[3] Univ Illinois, Dept Math, Urbana, IL 61801 USA

[4] Univ Zagreb, Dept Math, Zagreb 41000, Croatia

来源：

POTENTIAL ANALYSIS | 2014年 / 41卷 / 02期

基金：

新加坡国家研究基金会;

关键词：

Levy processes; Subordinate Brownian motion; Harmonic functions; Boundary Harnack principle; Martin kernel; Martin boundary; Poisson kernel;

D O I：

10.1007/s11118-013-9375-4

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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 kappa-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.

引用

页码：407 / 441

页数：35

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