{
  "id": "1304.0702",
  "version": "v2",
  "published": "2013-04-02T17:20:55.000Z",
  "updated": "2014-03-27T10:04:59.000Z",
  "title": "The Riesz transform for the harmonic oscillator in spherical coordinates",
  "authors": [
    "Ó. Ciaurri",
    "L. Roncal"
  ],
  "comment": "19 pages. To appear in Constructive Approximation",
  "categories": [
    "math.CA",
    "math.FA"
  ],
  "abstract": "In this paper we show weighted estimates in mixed norm spaces for the Riesz transform associated with the harmonic oscillator in spherical coordinates. In order to prove the result we need a weighted inequality for a vector-valued extension of the Riesz transform related to the Laguerre expansions which is of independent interest. The main tools to obtain such extension are a weighted inequality for the Riesz transform independent of the order of the involved Laguerre functions and an appropriate adaptation of Rubio de Francia's extrapolation theorem.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-03-27T10:04:59.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "harmonic oscillator",
      "spherical coordinates",
      "francias extrapolation theorem",
      "riesz transform independent",
      "weighted inequality"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1304.0702C"
    }
  }
}