On fractional parabolic $\text{BMO}$ and ${\text{Lip}}_{\alpha }$ caloric capacities

In the present paper we characterize the removable sets for solutions of the fractional heat equation satisfying some parabolic $\text{BMO}$ or ${\text{Lip}}_{\alpha }$ normalization conditions. We do this by introducing associated fractional caloric capacities, that we show to be comparable to a certain parabolic Hausdorff content.