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The Besov capacity in metric spaces

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Nuutinen, J. (2016). The Besov capacity in metric spaces. Annales Polonici Mathematici, 117 (1), 59-78. doi:10.4064/ap3843-4-2016
Published in
Annales Polonici Mathematici
Authors
Nuutinen, Juho
Date
2016
Discipline
Matematiikka
Copyright
© 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.
Publisher
Polska Akademia Nauk
ISSN Search the Publication Forum
0066-2216
Keywords
Besov spaces capacity metric spaces
DOI
https://doi.org/10.4064/ap3843-4-2016
URI

http://urn.fi/URN:NBN:fi:jyu-201608023719

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