On the Poisson transform on a homogenous vector bundle over the quaternionic hyperbolic space

Achraf Ouald Chaib

doi:10.5802/crmath.550

Article de recherche - Analyse harmonique

On the Poisson transform on a homogenous vector bundle over the quaternionic hyperbolic space

Achraf Ouald Chaib ¹

¹ Department of Mathematics, Faculty of Sciences, University Ibn Tofail, Kénitra, Morocco

Comptes Rendus. Mathématique, Volume 362 (2024), pp. 265-273.

Résumé

Let $K \times_{M} V$ be the homogenous vector bundle over $K / M = S p (n) \times S p (1) / S p (n - 1) \times S p (1)$ associated to an irreducible representation $(δ_{ν}, V)$ of Sp(1). We give an image characterization of the Poisson transform $𝒫_{λ, ν}$ of $L^{2}$ -section of $K \times_{M} V$ . We also show that $𝒫_{λ, ν} f$ , $f$ $\in L^{p} (K \times_{M} V)$ satisfies a Hardy-type estimate.

Reçu le : 2023-06-02
Révisé le : 2023-07-21
Accepté le : 2023-07-24
Publié le : 2024-05-02

DOI : 10.5802/crmath.550

Affiliations des auteurs :

Achraf Ouald Chaib ¹

¹ Department of Mathematics, Faculty of Sciences, University Ibn Tofail, Kénitra, Morocco

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     title = {On the {Poisson} transform on a homogenous vector bundle over the quaternionic hyperbolic space},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {265--273},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {362},
     year = {2024},
     doi = {10.5802/crmath.550},
     language = {en},
}

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Achraf Ouald Chaib. On the Poisson transform on a homogenous vector bundle over the quaternionic hyperbolic space. Comptes Rendus. Mathématique, Volume 362 (2024), pp. 265-273. doi : 10.5802/crmath.550. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.550/

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