The Besov Capacity In Metric Spaces

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 $γ$-medians, for which we also prove a new version of a Poincaré type inequality.

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