On the (1/2,+)-caloric capacity of Cantor sets - Hernández, Joan (Annales Fennici Mathematici, 2024)
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 \(R^n+1\). The results obtained for the latter are analogous to those found for Newtonian capacity. Moreover, we also characterize the BMO and Lip\(_α\) variants (\(0<α<1\)) of the 1/2-caloric capacity in terms of the Hausdorff contents \(H^n_∞\) and \(H^n+α_∞\) respectively.