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 ${\text{Lip}}_{\alpha }$ variants ($0<\alpha <1$) of the $1/2$-caloric capacity in terms of the Hausdorff contents ${\mathcal{H}}_{\infty }^n$ and ${\mathcal{H}}_{\infty }^{n+\alpha }$ respectively.

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