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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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https://hal-cnrs.archives-ouvertes.fr/hal-03527893
Contributor : Khalid Koufany Connect in order to contact the contributor
Submitted on : Sunday, January 16, 2022 - 9:29:28 PM
Last modification on : Wednesday, August 10, 2022 - 11:12:07 AM
Long-term archiving on: : Sunday, April 17, 2022 - 6:11:41 PM

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  • HAL Id : hal-03527893, version 1

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

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