{
  "id": "2002.12264",
  "version": "v1",
  "published": "2020-02-27T17:07:06.000Z",
  "updated": "2020-02-27T17:07:06.000Z",
  "title": "Average radial integrability spaces of analytic functions",
  "authors": [
    "Tanausu Aguilar-Hernandez",
    "Manuel D. Contreras",
    "Luis Rodriguez-Piazza"
  ],
  "comment": "31 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "In this paper we introduce the family of spaces $RM(p,q)$, $1\\leq p,q\\leq +\\infty$. They are spaces of holomorphic functions in the unit disc with average radial integrability. This family contains the classical Hardy spaces (when $p=\\infty$) and Bergman spaces (when $p=q$). We characterize the inclusion between $RM(p_1,q_1)$ and $RM(p_2,q_2)$ depending on the parameters. For $1<p,q<\\infty$, our main result provides a characterization of the dual spaces of $RM(p,q)$ by means of the boundedness of the Bergman projection. We show that $RM(p,q)$ is separable if and only if $q<+\\infty$. In fact, we provide a method to build isomorphic copies of $\\ell^\\infty$ in $RM(p,\\infty)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-02-27T17:07:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "30H20",
      "47B33",
      "47D06",
      "46E15",
      "47G10"
    ],
    "keywords": [
      "average radial integrability spaces",
      "analytic functions",
      "build isomorphic copies",
      "classical hardy spaces",
      "bergman spaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 31,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}