Capacities Characterizing Removable Sets for Various Function Spaces in Carnot Groups

We study removable sets for the Campanato, Hölder continuous, $L_{\text{loc}}^p$, and Lipschitz functions in Carnot groups. In the former three cases, we characterize removability through the use of capacities with respect to any left-invariant linear differential operator $\mathcal{L}$ for which $\mathcal{L}$ and ${\mathcal{L}}^t$ are hypoelliptic and satisfy a homogeneity condition, while in the latter case we characterize Lipschitz functions with respect to the sub-Laplacian.