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

Michael J. Puls
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Abstract

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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Michael J. Puls. 2005-09-07. The first $L^p$-cohomology of some finitely generated groups and $p$-harmonic functions. https://arxiv.org/abs/math/0509170

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