Null sets for the capacity associated to Riesz kernels

Abstract

We prove that the capacity associated to the signed vector-valued Riesz kernel $\frac{x}{|x|^{1+\alpha}}$ in $\Rn$, $0<\alpha<n$, $\alpha\notin\Z$, vanishes on compact sets with finite $\alpha$-Hausdorff measure that satisfy an additional density condition.