{
  "id": "2112.09994",
  "version": "v3",
  "published": "2021-12-18T20:18:08.000Z",
  "updated": "2024-11-08T12:49:31.000Z",
  "title": "On Poisson transforms of differential forms on real hyperbolic spaces",
  "authors": [
    "Salem Bensaïd",
    "Abdelhamid Boussejra",
    "Khalid Koufany"
  ],
  "categories": [
    "math.RT",
    "math.DG"
  ],
  "abstract": "This paper is concerned with the Poisson transform of differential forms on the hyperbolic space $H^n(\\mathbb R)$. Consider an integer $p$ such that $1\\leqslant p\\leqslant n$ and let $q$ be either $p-1$ or $p$. For $1<r<\\infty$, we prove that the Poisson transform is a topological isomorphism from the space of $L^r$-differential $q$-forms on the boundary $\\partial H^n(\\mathbb R)$ onto a Hardy-type subspace of $p$-eigenforms of the Hodge-de Rham Laplacian on $H^n(\\mathbb R)$.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2024-11-08T12:49:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "58A10",
      "43A85",
      "53C35",
      "22E30"
    ],
    "keywords": [
      "real hyperbolic spaces",
      "poisson transform",
      "differential forms",
      "hodge-de rham laplacian",
      "hardy-type subspace"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}