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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2410.06592 |
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| _version_ | 1866909343048269824 |
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| author | Baldi, Annalisa Franchi, Bruno Pansu, Pierre |
| author_facet | Baldi, Annalisa Franchi, Bruno Pansu, Pierre |
| contents | In the Euclidean space it is known that a function $f\in L^2$ of a ball, with vanishing average,is the divergence of a vector field $F\in L^2$ with$$\| F\|\_{ L^2(B)} \le C \|f\|\_{L^2(B)}.$$In this Note we prove a similar result in any Carnot group $\mathbb{G}$ for a vanishing average $f\in L^p$, $1\le p < Q$, where $Q$ is the so-called homogeneous dimension of $\mathbb{G}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_06592 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Primitives of volume forms in Carnot groups Baldi, Annalisa Franchi, Bruno Pansu, Pierre Analysis of PDEs In the Euclidean space it is known that a function $f\in L^2$ of a ball, with vanishing average,is the divergence of a vector field $F\in L^2$ with$$\| F\|\_{ L^2(B)} \le C \|f\|\_{L^2(B)}.$$In this Note we prove a similar result in any Carnot group $\mathbb{G}$ for a vanishing average $f\in L^p$, $1\le p < Q$, where $Q$ is the so-called homogeneous dimension of $\mathbb{G}$. |
| title | Primitives of volume forms in Carnot groups |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2410.06592 |