On the (1/2,+)-caloric capacity of Cantor sets

Abstract

In the present paper we characterize the (1/2,+)-caloric capacity (associated with the 1/2-fractional heat equation) of the usual corner-like Cantor set of ${\mathbb{R}}^{n+1}$. The results obtained for the latter are analogous to those found for Newtonian capacity. Moreover, we also characterize the BMO and Lip${}_{\alpha }$ variants ($0<\alpha <1$) of the 1/2-caloric capacity in terms of the Hausdorff contents $H_{\mathrm{\infty }}^n$ and $H_{\mathrm{\infty }}^{n+\alpha }$ respectively.