The Riesz Capacity in Metric Spaces

2015/01/23 by Nuutinen, Juho, Silvestre, Pilar
#31B15 #31E05 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1501.05746

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.

Related

• Capacities and density conditions in metric spaces
• Classifying Triebel-Lizorkin capacities in metric spaces
• Riesz Type Potentials in the framework of quasi-metric spaces equipped with upper doubling measures
• Hausdorff measure and decay rate of Riesz capacity
• Triebel-Lizorkin capacity and Hausdorff measure in metric spaces