On Poisson transforms of differential forms on real hyperbolic spaces

We study the Poisson transform of differential forms on the hyperbolic space $H^{n} (ℝ)$ . Let us consider an integer $p$ such that $1 \leq p \leq n$ 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 $\partial H^{n} (ℝ)$ onto a Hardy-type subspace of $p$ -eigenforms of the Hodge–de Rham Laplacian on $H^{n} (ℝ)$ .

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Keywords

real hyperbolic space, Poisson transform, eigenform, differential form

Mathematical Subject Classification

Primary: 22E30, 43A85, 53C35, 58A10

Milestones

Received: 11 November 2024

Revised: 26 January 2025

Accepted: 11 February 2025

Published: 14 February 2026

Authors

Salem Ben Saïd
Department of Mathematical Sciences College of Science United Arab Emirates University Al Ain United Arab Emirates

Abdelhamid Boussejra
Department of Mathematics University Ibn Tofail Kenitra Morocco

Khalid Koufany
Université de Lorraine CNRS, IECL Nancy France

Vol. 8, No. 1, 2026

Salem Ben Saïd, Abdelhamid Boussejra and Khalid Koufany

Abstract

PDF Access Denied

Keywords

Mathematical Subject Classification

Milestones

Authors