3G-inequality for planar domains
成果类型：
Article
署名作者：
Hansen, Wolfhard
署名单位：
University of Bielefeld
刊物名称：
PROBABILITY THEORY AND RELATED FIELDS
ISSN/ISSBN：
0178-8051
DOI：
10.1007/s00440-010-0335-2
发表日期：
2012
页码：
357-366
关键词：
摘要：
The 3G-inequality for Green functions g(D) on arbitrary bounded domains in R-2, which Bass and Burdzy (Probab Theory Relat Fields 101(4): 479- 493, 1995) obtained by a genuinely probabilistic proof (using loops of Brownian motion around the origin), is proven (in a more precise form) employing elementary properties of harmonic measures only. Since harmonic measures are hitting distributions of Brownian motion, this purely analytic proof can be viewed as well as being probabilistic. A spin- off is an upper estimate of gD on subdisks B' of an open disk B in terms of gB divided by the capacity of B' \ D with respect to B.