The $p$-harmonic boundary and $D_p$-massive subsets of a graph of bounded degree

Details The $p$-harmonic boundary and $D_p$-massive subsets of a graph of bounded degree The $p$-harmonic boundary and $D_p$-massive subsets of a graph of bounded degree

2011-08-22

arxiv.org/abs/1108.4381v1

Mathematics

Functional Analysis

Scientific paper

Let $p$ be a real number greater than one and let $\Gamma$ be a graph of bounded degree. We investigate links between the $p$-harmonic boundary of $\Gamma$ and the $D_p$-massive subsets of $\Gamma$. In particular, we show that if the $p$-haromonic boundary is finite, then there is a bijection from the $p$-harmonic boundary to a maximal collection of pairwise disjoint $D_p$-massive sets that satisfy a certain property.

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