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

Ouald Chaib, Achraf

Comptes Rendus. Mathématique, Tome 362 (2024) no. G3, pp. 265-273

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

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