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On Poisson transforms for differential forms on real hyperbolic spaces

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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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Dates and versions

hal-03527893 , version 1 (16-01-2022)

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  • HAL Id : hal-03527893 , version 1

Cite

Salem Bensaïd, Abdelhamid Boussejra, Khalid Koufany. On Poisson transforms for differential forms on real hyperbolic spaces. 2022. ⟨hal-03527893⟩
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