Estimates and structure of α-harmonic functions

• 成果类型: Article
• 署名作者: Bogdan, Krzysztof; Kulczycki, Tadeusz; Kwasnicki, Mateusz
• 署名单位: Wroclaw University of Science & Technology; Purdue University System; Purdue University
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-007-0067-0
• 发表日期: 2008
• 页码: 345-381
• 关键词: boundary harnack principle; symmetric stable processes; martin boundary; green-function; THEOREM

摘要

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 boolean OR {infinity} satisfying an integrability condition. The corresponding Martin boundary of D is a subset of the Euclidean boundary determined by an integral test.