English

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 LpL^p 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

R2 v1 2026-07-01T11:45:00.128Z