{
  "id": "1712.04634",
  "version": "v1",
  "published": "2017-12-13T07:28:46.000Z",
  "updated": "2017-12-13T07:28:46.000Z",
  "title": "Characterisation of the L p Range of the Gen- eralised Poisson Transform of the hyperbolic space B(H n )",
  "authors": [
    "Imane Ghanimi"
  ],
  "categories": [
    "math.CA"
  ],
  "abstract": "The aim of this paper is to give the characterisation of the L p Range (p $\\ge$ 2) of the Generalised Poisson Transform of the Hyperbolic space B(H n), (n $\\ge$ 2), over the classical field of the quaternions H. Namely, if f is an hyperfunction in the boundary of B(H n), then we show that f is in L p ($\\partial$B(H n)) if and only if it's generalised poisson transform satisfy an Hardy type growth condition. An explicit expression of the generalized spherical functions is given. Mathematics Subject Classification (2010). Primary 22E46; Secondary 33Cxx.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-12-13T07:28:46.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hyperbolic space",
      "characterisation",
      "hardy type growth condition",
      "mathematics subject classification",
      "generalised poisson transform satisfy"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}