The first $L^p$-cohomology of some finitely generated groups and $p$-harmonic functions

Details The first $L^p$-cohomology of some finitely generated groups and $p$-harmonic functions The first $L^p$-cohomology of some finitely generated groups and $p$-harmonic functions

2005-09-07

arxiv.org/abs/math/0509170v1

Mathematics

Functional Analysis

Scientific paper

Let $G$ be a finitely generated infinite group and let $p > 1$. In this paper
we make a connection between the first $L^p$-cohomology space of $G$ and
$p$-harmonic functions on $G$. We also describe the elements in the first
$L^p$-cohomology space of groups with polynomial growth, and we give an
inclusion result for nonamenable groups.

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