Fatou theorem of p-harmonic functions on trees

Robert Kaufman, Jang Mei Wu

Research output: Contribution to journalArticle

Abstract

We study bounded p-harmonic functions u defined on a directed tree T with branching order k(1 < p < ∞ and K = 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 u 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 k fixed); the infimum d(k, p) is attained and is strictly between 0 and 1 expect when p = 2 or k = 2.

Original languageEnglish (US)
Pages (from-to)1138-1148
Number of pages11
JournalAnnals of Probability
Volume28
Issue number3
DOIs
StatePublished - Jul 2000

Keywords

  • Dimension
  • Entropy
  • Fatou theorem
  • P-harmonic functions
  • Trees

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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