The Besov Capacity In Metric Spaces

Abstract

We study a capacity theory based on a definition of Hajł asz-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.

References in corpus (2)

• The Riesz Capacity in Metric Spaces
• Approximation by Hölder functions in Besov and Triebel-Lizorkin spaces

Cited by in corpus (1)

• A gradient estimate for nonlocal minimal graphs