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arXiv · 1501.05746

The Riesz Capacity in Metric Spaces

Juho Nuutinen·Pilar Silvestre
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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.

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Juho Nuutinen, Pilar Silvestre. 2015-10-28. The Riesz Capacity in Metric Spaces. https://arxiv.org/abs/1501.05746

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