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 $1/2<s\le 1$. 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.

References in corpus (1)

• Carleson measure estimates for caloric functions and parabolic uniformly rectifiable sets