The Riesz Capacity in Metric Spaces
Functional Analysis
2015-10-30 v2 Classical Analysis and ODEs
Abstract
We study a capacity theory based on a definition of a Riesz potential in metric spaces with a doubling measure. In this general setting, we study the basic properties of the Riesz capacity, including monotonicity, countable subadditivity and several convergence results. We define a modified version of the Hausdorff measure and provide lower bound and upper bound estimates for the capacity in terms of the modified Hausdorff content.
Keywords
Cite
@article{arxiv.1501.05746,
title = {The Riesz Capacity in Metric Spaces},
author = {Juho Nuutinen and Pilar Silvestre},
journal= {arXiv preprint arXiv:1501.05746},
year = {2015}
}