{
  "id": "0807.2981",
  "version": "v1",
  "published": "2008-07-18T14:33:24.000Z",
  "updated": "2008-07-18T14:33:24.000Z",
  "title": "The Littlewood--Paley--Rubio de Francia property of a Banach space for the case of equal intervals",
  "authors": [
    "T. P. Hytönen",
    "J. L. Torrea",
    "D. V. Yakubovich"
  ],
  "comment": "To appear in The Royal Society of Edinburgh Proc. A (Mathematics)",
  "journal": "Proc. Roy. Soc. Edinburgh Sect. A 139 (2009), no. 4, 819-832",
  "categories": [
    "math.FA"
  ],
  "abstract": "Let $X$ be a Banach space. It is proved that an analogue of the Rubio de Francia square function estimate for partial sums of the Fourier series of $X$-valued functions holds true for all disjoint collections of subintervals of the set of integers of equal length and for all exponents $p$ greater or equal than 2 if and only if the space $X$ is a UMD space of type 2. The same criterion is obtained for the case of subintervals of the real line and Fourier integrals instead of Fourier series.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-07-18T14:33:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42Bxx",
      "46B20"
    ],
    "keywords": [
      "banach space",
      "equal intervals",
      "francia property",
      "littlewood-paley-rubio",
      "fourier series"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0807.2981H"
    }
  }
}