Fatou Theorem of p-harmonic functions on trees
成果类型：
Article
署名作者：
Kaufman, R; Wu, JM
署名单位：
University of Illinois System; University of Illinois Urbana-Champaign
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
DOI：
10.1214/aop/1019160328
发表日期：
2000
页码：
1138-1148
关键词：
摘要：
We study bounded p-harmonic functions u defined on a directed tree T with branching order kappa (1 < p < infinity and kappa = 2, 3,...). Denote by BV(u) the set of paths on which u has finite variation and F(u) the set of paths on which rr has a finite limit. Then the infimum of dim BV(u) and the infimum of dim F(u) are equal over all bounded p-harmonic functions on T (with p and kappa fixed); the infimum d(kappa, p) is attained and is strictly between 0 and 1 expect when p = 2 or kappa = 2.
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