Characterizations of Sobolev and BV functions on Carnot groups
Functional Analysis
2026-04-01 v1
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 Taylor approximation, in the spirit of the results by Bourgain, Brezis and Mironescu.
Cite
@article{arxiv.2603.28996,
title = {Characterizations of Sobolev and BV functions on Carnot groups},
author = {Francesco Serra Cassano and Kilian Zambanini},
journal= {arXiv preprint arXiv:2603.28996},
year = {2026}
}
Comments
38 pages