{
  "id": "1703.07859",
  "version": "v1",
  "published": "2017-03-22T21:20:06.000Z",
  "updated": "2017-03-22T21:20:06.000Z",
  "title": "Bergman-Lorentz spaces on tube domains over symmetric cones",
  "authors": [
    "David Bekolle",
    "Jocelyn",
    "Cyrille Nana"
  ],
  "comment": "23 pages",
  "categories": [
    "math.CA"
  ],
  "abstract": "We study Bergman-Lorentz spaces on tube domains over symmetric cones, i.e. spaces of holomorphic functions which belong to Lorentz spaces $L(p, q).$ We establish boundedness and surjectivity of Bergman projectors from Lorentz spaces to the corresponding Bergman-Lorentz spaces and real interpolation between Bergman-Lorentz spaces. Finally we ask a question whose positive answer would enlarge the interval of parameters $p\\in (1, \\infty)$ such that the relevant Bergman projector is bounded on $L^p$ for cones of rank $r\\geq 3.$",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-03-22T21:20:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "32A25",
      "32M11",
      "46B70",
      "46E30"
    ],
    "keywords": [
      "tube domains",
      "symmetric cones",
      "study bergman-lorentz spaces",
      "relevant bergman projector",
      "corresponding bergman-lorentz spaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}