On Poisson transforms for differential forms on real hyperbolic spaces
Abstract
We study the Poisson transform for differential forms on the real hyperbolic space H^n. For 1 < r < ∞, we prove that the Poisson transform is a topological isomorphism from the space of L r differential q-forms on the boundary ∂H^n onto a Hardy-type subspace of p-eigenforms of the Hodge-de Rham Laplacian on H^n , for 0 ≤ p < n−1 2 and q ∈ {p − 1, p}.
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