On the semiadditivity of the capacities associated with signed vector valued Riesz kernels

TL;DR

This paper proves the semiadditivity property of capacities linked to signed vector-valued Riesz kernels of a specific homogeneity in Euclidean space, advancing understanding of potential theory and harmonic analysis.

Contribution

It establishes the semiadditivity of capacities associated with signed vector-valued Riesz kernels of homogeneity -α in ℝ^n, a significant theoretical result.

Findings

Proves semiadditivity of capacities for signed vector Riesz kernels

Extends potential theory to vector-valued kernel capacities

Provides foundational results for harmonic analysis and capacity theory

Abstract

The aim of this paper is to show the semiadditivity of the capacities associated to the signed vector valued Riesz kernels of homogeneity $-\alpha$ in $\mathbb{R}^n$, with $0<\alpha<n$.