The fractional Lipschitz caloric capacity of Cantor sets

Abstract

We characterize the s-parabolic Lipschitz caloric capacity of corner-like $s$-parabolic Cantor sets in $\mathbb{R}^{n+1}$ for $1/2<s\leq 1$. Despite the spatial gradient of the s-heat kernel lacking temporal anti-symmetry, we obtain analogous results to those known for analytic and Riesz capacities.