The Besov capacity in metric spaces
Tom 117 / 2016
Annales Polonici Mathematici 117 (2016), 59-78 MSC: Primary 31E05; Secondary 31B15. DOI: 10.4064/ap3843-4-2016 Opublikowany online: 17 June 2016
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 $\gamma $-medians, for which we also prove a new version of a Poincaré type inequality.