On Poisson transforms of differential forms on real hyperbolic spaces
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2021
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| _version_ | 1866910688286343168 |
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| author | Bensaïd, Salem Boussejra, Abdelhamid Koufany, Khalid |
| author_facet | Bensaïd, Salem Boussejra, Abdelhamid Koufany, Khalid |
| contents | This paper is concerned with the Poisson transform of differential forms on the hyperbolic space $H^n(\mathbb R)$. Consider an integer $p$ such that $1\leqslant p\leqslant n$ and let $q$ be either $p-1$ or $p$. For $1<r<\infty$, we prove that the Poisson transform is a topological isomorphism from the space of $L^r$-differential $q$-forms on the boundary $\partial H^n(\mathbb R)$ onto a Hardy-type subspace of $p$-eigenforms of the Hodge-de Rham Laplacian on $H^n(\mathbb R)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2112_09994 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | On Poisson transforms of differential forms on real hyperbolic spaces Bensaïd, Salem Boussejra, Abdelhamid Koufany, Khalid Representation Theory Differential Geometry 58A10, 43A85, 53C35, 22E30 This paper is concerned with the Poisson transform of differential forms on the hyperbolic space $H^n(\mathbb R)$. Consider an integer $p$ such that $1\leqslant p\leqslant n$ and let $q$ be either $p-1$ or $p$. For $1<r<\infty$, we prove that the Poisson transform is a topological isomorphism from the space of $L^r$-differential $q$-forms on the boundary $\partial H^n(\mathbb R)$ onto a Hardy-type subspace of $p$-eigenforms of the Hodge-de Rham Laplacian on $H^n(\mathbb R)$. |
| title | On Poisson transforms of differential forms on real hyperbolic spaces |
| topic | Representation Theory Differential Geometry 58A10, 43A85, 53C35, 22E30 |
| url | https://arxiv.org/abs/2112.09994 |