Geodesic
The Besov capacity in metric spaces
Juho Nuutinen1
1 Department of Mathematics and Statistics P.O. Box 35 University of Jyväskylä, FI-40014, Finland
Annales Polonici Mathematici, Tome 117 (2016) no. 1, pp. 59-78.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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.
DOI : 10.4064/ap3843-4-2016
Keywords: study capacity theory based definition haj asz besov functions prove several properties capacity general setting metric space equipped doubling measure main results paper lower bound upper bound estimates capacity terms modified netrusov hausdorff content important tools gamma medians which prove version poincar type inequality

Juho Nuutinen 1

1 Department of Mathematics and Statistics P.O. Box 35 University of Jyväskylä, FI-40014, Finland 
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Juho Nuutinen. The Besov capacity in metric spaces. Annales Polonici Mathematici, Tome 117 (2016) no. 1, pp. 59-78. doi : 10.4064/ap3843-4-2016. http://geodesic.mathdoc.fr/articles/10.4064/ap3843-4-2016/

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