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 \(H^n_\infty\) and \(H^{n+\alpha}_\infty\) respectively.