On Poisson transforms for differential forms on real hyperbolic spaces

Salem Bensaïd (1) , Abdelhamid Boussejra (2) , Khalid Koufany (3)

1 UAEU - United Arab Emirates University
2 UIT - Université Ibn Tofaïl
3 IECL - Institut Élie Cartan de Lorraine

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}.

Mots clés: Poisson transform; Hyperforms; Differential forms; Real hyperbolic space; Fatou type theorem

Domaines: Théorie des représentations [math.RT]; Géométrie différentielle [math.DG]

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