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July 2000 Fatou theorem of p-harmonic functions on trees
Robert Kaufman, Jang-Mei Wu
Ann. Probab. 28(3): 1138-1148 (July 2000). DOI: 10.1214/aop/1019160328

Abstract

We study bounded $p$-harmonic functions $u$ defined on a directed tree $T$ with branching order $\kappa(1<p<\infty$ \and $\kappa=2,3,\ldots)$. Denote by $BV(u)$ the set of paths on which $u$ has finite variation and $\mathscr{F}(u)$ the set of paths on which $u$ has a finite limit. Then the infimum of dim $BV(u)$ and the infimum of dim $\mathscr{F}(u)$ are equal over all bounded-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 $\kappa = 2$.

Citation

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Robert Kaufman. Jang-Mei Wu. "Fatou theorem of p-harmonic functions on trees." Ann. Probab. 28 (3) 1138 - 1148, July 2000. https://doi.org/10.1214/aop/1019160328

Information

Published: July 2000
First available in Project Euclid: 18 April 2002

zbMATH: 1038.31007
MathSciNet: MR1797306
Digital Object Identifier: 10.1214/aop/1019160328

Subjects:
Primary: 31C20, 31C45
Secondary: 31A20, 60G42

Rights: Copyright © 2000 Institute of Mathematical Statistics

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Vol.28 • No. 3 • July 2000
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