{
  "id": "1705.07792",
  "version": "v1",
  "published": "2017-05-22T15:02:03.000Z",
  "updated": "2017-05-22T15:02:03.000Z",
  "title": "Fourier multipliers in Banach function spaces with UMD concavifications",
  "authors": [
    "Alex Amenta",
    "Emiel Lorist",
    "Mark Veraar"
  ],
  "categories": [
    "math.FA",
    "math.CA"
  ],
  "abstract": "We prove various extensions of the Coifman-Rubio de Francia-Semmes multiplier theorem to operator-valued multipliers on Banach function spaces. Our results involve a new boundedness condition on sets of operators which we call $\\ell^{r}(\\ell^{s})$-boundedness, which implies $\\mathcal{R}$-boundedness in many cases. The proofs are based on new Littlewood-Paley-Rubio de Francia-type estimates in Banach function spaces which were recently obtained by the authors.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-05-22T15:02:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B15",
      "42B25",
      "46E30",
      "47A56"
    ],
    "keywords": [
      "banach function spaces",
      "fourier multipliers",
      "umd concavifications",
      "francia-semmes multiplier theorem",
      "francia-type estimates"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}