{
  "id": "0805.1053",
  "version": "v1",
  "published": "2008-05-07T20:14:09.000Z",
  "updated": "2008-05-07T20:14:09.000Z",
  "title": "Uniform rectifiability, Calderon-Zygmund operators with odd kernel, and quasiorthogonality",
  "authors": [
    "Xavier Tolsa"
  ],
  "comment": "34 pages",
  "doi": "10.1112/plms/pdn035",
  "categories": [
    "math.CA",
    "math.FA"
  ],
  "abstract": "In this paper we study some questions in connection with uniform rectifiability and the $L^2$ boundedness of Calderon-Zygmund operators. We show that uniform rectifiability can be characterized in terms of some new adimensional coefficients which are related to the Jones' $\\beta$ numbers. We also use these new coefficients to prove that n-dimensional Calderon-Zygmund operators with odd kernel of type $C^2$ are bounded in $L^2(\\mu)$ if $\\mu$ is an n-dimensional uniformly rectifiable measure.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-05-07T20:14:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "28A75",
      "42B20"
    ],
    "keywords": [
      "uniform rectifiability",
      "odd kernel",
      "quasiorthogonality",
      "n-dimensional calderon-zygmund operators",
      "adimensional coefficients"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 34,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0805.1053T"
    }
  }
}