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arXiv · 2603.28996

Characterizations of Sobolev and BV functions on Carnot groups

Francesco Serra Cassano·Kilian Zambanini
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Abstract

We establish two characterizations of real-valued Sobolev and BV functions on Carnot groups. The first is obtained via a nonlocal approximation of the distributional horizontal gradient, while the second is based on an $L^p$ Taylor approximation, in the spirit of the results by Bourgain, Brezis and Mironescu.

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Francesco Serra Cassano, Kilian Zambanini. 2026-03-30. Characterizations of Sobolev and BV functions on Carnot groups. https://arxiv.org/abs/2603.28996

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