On the Poisson transform on a homogenous vector bundle over the quaternionic hyperbolic space
Let $K\times _M V$ be the homogenous vector bundle over $K/M=Sp(n)\times Sp(1)/Sp(n-1)\times Sp(1)$ associated to an irreducible representation $(\delta _{\nu }, V)$ of Sp(1). We give an image characterization of the Poisson transform $\mathcal{P}_{\lambda ,\nu }$ of $L^{2}$-section of $K\times _M V...
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Académie des sciences
2024-05-01
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| Series: | Comptes Rendus. Mathématique |
| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.550/ |
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| author | Ouald Chaib, Achraf |
| author_facet | Ouald Chaib, Achraf |
| author_sort | Ouald Chaib, Achraf |
| collection | DOAJ |
| description | Let $K\times _M V$ be the homogenous vector bundle over $K/M=Sp(n)\times Sp(1)/Sp(n-1)\times Sp(1)$ associated to an irreducible representation $(\delta _{\nu }, V)$ of Sp(1). We give an image characterization of the Poisson transform $\mathcal{P}_{\lambda ,\nu }$ of $L^{2}$-section of $K\times _M V$. We also show that $\mathcal{P}_{\lambda ,\nu }f$, $f$ $\in L^{p}(K\times _M V) $ satisfies a Hardy-type estimate. |
| format | Article |
| id | doaj-art-d217a0d68b604ddbab56eabd634b7d9d |
| institution | Kabale University |
| issn | 1778-3569 |
| language | English |
| publishDate | 2024-05-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj-art-d217a0d68b604ddbab56eabd634b7d9d2025-02-07T11:19:53ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692024-05-01362G326527310.5802/crmath.55010.5802/crmath.550On the Poisson transform on a homogenous vector bundle over the quaternionic hyperbolic spaceOuald Chaib, Achraf0Department of Mathematics, Faculty of Sciences, University Ibn Tofail, Kénitra, MoroccoLet $K\times _M V$ be the homogenous vector bundle over $K/M=Sp(n)\times Sp(1)/Sp(n-1)\times Sp(1)$ associated to an irreducible representation $(\delta _{\nu }, V)$ of Sp(1). We give an image characterization of the Poisson transform $\mathcal{P}_{\lambda ,\nu }$ of $L^{2}$-section of $K\times _M V$. We also show that $\mathcal{P}_{\lambda ,\nu }f$, $f$ $\in L^{p}(K\times _M V) $ satisfies a Hardy-type estimate.https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.550/ |
| spellingShingle | Ouald Chaib, Achraf On the Poisson transform on a homogenous vector bundle over the quaternionic hyperbolic space Comptes Rendus. Mathématique |
| title | On the Poisson transform on a homogenous vector bundle over the quaternionic hyperbolic space |
| title_full | On the Poisson transform on a homogenous vector bundle over the quaternionic hyperbolic space |
| title_fullStr | On the Poisson transform on a homogenous vector bundle over the quaternionic hyperbolic space |
| title_full_unstemmed | On the Poisson transform on a homogenous vector bundle over the quaternionic hyperbolic space |
| title_short | On the Poisson transform on a homogenous vector bundle over the quaternionic hyperbolic space |
| title_sort | on the poisson transform on a homogenous vector bundle over the quaternionic hyperbolic space |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.550/ |
| work_keys_str_mv | AT oualdchaibachraf onthepoissontransformonahomogenousvectorbundleoverthequaternionichyperbolicspace |