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 an 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, for 0 ≤ p < n−1 2 and q = p − 1, p.