preprint

Inserted: 1 apr 2026

Year: 2026

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.