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The Besov capacity in metric spaces

Volume 117 / 2016

Juho Nuutinen Annales Polonici Mathematici 117 (2016), 59-78 MSC: Primary 31E05; Secondary 31B15. DOI: 10.4064/ap3843-4-2016 Published online: 17 June 2016

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

Authors

  • Juho NuutinenDepartment of Mathematics and Statistics
    P.O. Box 35
    University of Jyväskylä, FI-40014, Finland
    e-mail

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