The Besov capacity in metric spaces
Nuutinen, J. (2016). The Besov capacity in metric spaces. Annales Polonici Mathematici, 117 (1), 59-78. doi:10.4064/ap3843-4-2016
Published inAnnales Polonici Mathematici
© Instytut Matematyczny PAN, 2016. Published in this repository with the kind permission of the publisher.
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.