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

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 \(Rⁿ⁺¹\). The results obtained for the latter are analogous to those found for Newtonian capacity. Moreover, we also characterize the BMO and Lip\(_α\) variants (\(0<α<1\)) of the 1/2-caloric capacity in terms of the Hausdorff contents \(H^n_∞\) and \(Hn+α_∞\) respectively.