Norms of spherical averaging operators for some geometric group actions

Abstract

We obtain asymptotic estimates for the ${\ell }^p$-operator norm of spherical averaging operators associated to certain geometric group actions. The motivating example is the case of Gromov hyperbolic groups, for which we obtain asymptotically sharp estimates. We deduce asymptotic lower bounds for the combinatorial expansion of spheres.

arXiv comment20 pages