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arXiv · 2512.17167

Capacities Characterizing Removable Sets for Various Function Spaces in Carnot Groups

Zack Boone
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Abstract

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.

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Zack Boone. 2025-12-19. Capacities Characterizing Removable Sets for Various Function Spaces in Carnot Groups. https://arxiv.org/abs/2512.17167

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