Abstract

We study the Poisson transform of differential forms on the hyperbolic space $H^n(ℝ)$. Let us consider an integer $p$ such that $1\le p\le n$ 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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