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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap3843-4-2016,
author = {Juho Nuutinen},
title = {The Besov capacity in metric spaces},
journal = {Annales Polonici Mathematici},
volume = {116},
year = {2016},
pages = {59-78},
zbl = {06602756},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap3843-4-2016}
}
Juho Nuutinen. The Besov capacity in metric spaces. Annales Polonici Mathematici, Tome 116 (2016) pp. 59-78. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap3843-4-2016/