The Besov capacity in metric spaces

Abstract

We study a capacity theory based on a definition of Hajłasz–Besov functions. We prove several properties of this capacity in the general setting of a metric space equipped with a doubling measure. The main results of the paper are lower bound and upper bound estimates for the capacity in terms of a modified Netrusov–Hausdorff content. Important tools are γ-medians, for which we also prove a new version of a Poincaré type inequality.