On the $(1\mathrm{/}2,+)$-caloric capacity of Cantor sets

In the present paper we characterize the $(1\mathrm{/}2,+)$-caloric capacity (associated with the $1\mathrm{/}2$-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 $1\mathrm{/}2$-caloric capacity in terms of the Hausdorff contents ${\mathcal{H}}_{\mathrm{\infty }}^n$ and ${\mathcal{H}}_{\mathrm{\infty }}^{n+\alpha }$ respectively.