{
  "id": "1810.12833",
  "version": "v1",
  "published": "2018-10-30T16:02:58.000Z",
  "updated": "2018-10-30T16:02:58.000Z",
  "title": "The $\\ell^s$-boundedness of a family of integral operators on UMD Banach function spaces",
  "authors": [
    "Emiel Lorist"
  ],
  "comment": "13 pages. Generalization of arXiv:1410.6657",
  "categories": [
    "math.FA",
    "math.CA"
  ],
  "abstract": "We prove the $\\ell^s$-boundedness of a family of integral operators with an operator-valued kernel on UMD Banach function spaces. This generalizes and simplifies earlier work by Gallarati, Veraar and the author, where the $\\ell^s$-boundedness of this family of integral operators was shown on Lebesgue spaces. The proof is based on a characterization of $\\ell^s$-boundedness as weighted boundedness by Rubio de Francia.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-10-30T16:02:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B20",
      "42B25",
      "46E30"
    ],
    "keywords": [
      "umd banach function spaces",
      "integral operators",
      "boundedness",
      "simplifies earlier work",
      "lebesgue spaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}