English

Capacities and Hausdorff measures on metric spaces

Functional Analysis 2014-08-27 v1

Abstract

In this article, we show that in a QQ-doubling space (X,d,μ),(X,d,\mu), Q>1,Q>1, that supports a QQ-Poincar\'e inequality and satisfies a chain condition, sets of QQ-capacity zero have generalized Hausdorff hh-measure zero for h(t)=log1Qϵ(1/t).h(t)=\log^{1-Q-\epsilon}(1/t).

Keywords

Cite

@article{arxiv.1408.5892,
  title  = {Capacities and Hausdorff measures on metric spaces},
  author = {Nijjwal Karak and Pekka Koskela},
  journal= {arXiv preprint arXiv:1408.5892},
  year   = {2014}
}

Comments

10 pages. arXiv admin note: substantial text overlap with arXiv:1408.5718