The first Lp-cohomology of some finitely generated groups and p-harmonic functions

Let G be a finitely generated infinite group and letp >1. In this paper we make a connection between the first Lp-cohomology space of G and p-harmonic functions on G. We also describe the elements in the first Lp-cohomology space of groups with polynomial growth, and we give an inclusion result for nonamenable groups. © 2006 Elsevier Inc. All rights reserved.