Characterizations of Sobolev and BV functions on Carnot groups
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866908923907276800 |
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| author | Cassano, Francesco Serra Zambanini, Kilian |
| author_facet | Cassano, Francesco Serra Zambanini, Kilian |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_28996 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Characterizations of Sobolev and BV functions on Carnot groups Cassano, Francesco Serra Zambanini, Kilian Functional Analysis 46E36 (Primary) 26B30, 35R03 (Secondary) 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. |
| title | Characterizations of Sobolev and BV functions on Carnot groups |
| topic | Functional Analysis 46E36 (Primary) 26B30, 35R03 (Secondary) |
| url | https://arxiv.org/abs/2603.28996 |