{
  "id": "math/0606006",
  "version": "v1",
  "published": "2006-05-31T21:56:25.000Z",
  "updated": "2006-05-31T21:56:25.000Z",
  "title": "Sharp estimates of martingale transforms in higher dimensions and applications to the Ahlfors-Beurling operator",
  "authors": [
    "Oliver Dragicevic",
    "Stefanie Petermichl",
    "Alexander Volberg"
  ],
  "comment": "41 pages, 12 figures",
  "categories": [
    "math.FA"
  ],
  "abstract": "The main aspiration of this note is to construct several different Haar-type systems in euclidean spaces of higher dimensions and prove sharp Lp bounds for the corresponding martingale transforms. In dimension one this was a result of Burkholder. The motivation for working in this direction is the search for Lp estimates of the Ahlfors-Beurling operator.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-05-31T21:56:25.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "higher dimensions",
      "ahlfors-beurling operator",
      "sharp estimates",
      "applications",
      "sharp lp bounds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 41,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......6006D"
    }
  }
}