{
  "id": "0809.3127",
  "version": "v1",
  "published": "2008-09-18T12:00:41.000Z",
  "updated": "2008-09-18T12:00:41.000Z",
  "title": "On the norm of the Beurling-Ahlfors operator in several dimensions",
  "authors": [
    "Tuomas Hytönen"
  ],
  "comment": "12 pages, submitted for publication",
  "categories": [
    "math.CA",
    "math.PR"
  ],
  "abstract": "The Lp operator norm of the generalized Beurling-Ahlfors transformation in n variables is at most (n/2+1)(p-1) for p>2. This improves on earlier results in all dimensions n>2. The proof is based on the heat extension and relies at the bottom on Burkholder's sharp inequality for martingale transforms.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-09-18T12:00:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B20",
      "60G46"
    ],
    "keywords": [
      "beurling-ahlfors operator",
      "dimensions",
      "lp operator norm",
      "burkholders sharp inequality",
      "earlier results"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0809.3127H"
    }
  }
}