Characterizations of Sobolev and BV functions on Carnot groups
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 Lp Taylor approximation, in the spirit of the results by Bourgain, Brezis and Mironescu.
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