We study removable sets for the Campanato, H\"{ o}lder continuous, $L^p_{ \text{ loc}}$, 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.
Categories: math.CA