{
  "id": "2404.07384",
  "version": "v1",
  "published": "2024-04-10T23:04:45.000Z",
  "updated": "2024-04-10T23:04:45.000Z",
  "title": "A~Moebius invariant space of $H$-harmonic functions on the ball",
  "authors": [
    "Petr Blaschke",
    "Miroslav Engliš",
    "El-Hassan Youssfi"
  ],
  "comment": "25 pages, no figures",
  "categories": [
    "math.CV",
    "math.FA"
  ],
  "abstract": "We~describe a Dirichlet-type space of $H$-harmonic functions, i.e. functions annihilated by the hyperbolic Laplacian on~the unit ball of the real $n$-space, as~the analytic continuation (in~the spirit of Rossi and Vergne) of the corresponding weighted Bergman spaces. Characterizations in terms of derivatives are given, and the associated semi-inner product is shown to be Moebius invariant. We~also give a formula for the corresponding reproducing kernel. Our~results solve an open problem addressed by M.~Stoll in his book ``Harmonic and subharmonic function theory on the hyperbolic ball'' (Cambridge University Press, 2016).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-04-10T23:04:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "31C05",
      "33C55",
      "32A36"
    ],
    "keywords": [
      "harmonic functions",
      "invariant space",
      "subharmonic function theory",
      "cambridge university press",
      "moebius invariant"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}