{
  "id": "1101.1734",
  "version": "v2",
  "published": "2011-01-10T08:54:14.000Z",
  "updated": "2011-09-02T14:21:18.000Z",
  "title": "Variation and oscillation for singular integrals with odd kernel on Lipschitz graphs",
  "authors": [
    "Albert Mas",
    "Xavier Tolsa"
  ],
  "comment": "38 pages",
  "doi": "10.1112/plms/pdr061",
  "categories": [
    "math.CA"
  ],
  "abstract": "We prove that, for r>2, the r-variation and oscillation for the smooth truncations of the Cauchy transform on Lipschitz graphs are bounded in L^p for 1<p finite. The analogous result holds for the n-dimensional Riesz transform on n-dimensional Lipschitz graphs, as well as for other singular integral operators with odd kernel. In particular, our results strengthen the classical theorem on the L^2 boundedness of the Cauchy transform on Lipschitz graphs by Coifman, McIntosh, and Meyer.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-09-02T14:21:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B20",
      "42B25"
    ],
    "keywords": [
      "odd kernel",
      "oscillation",
      "cauchy transform",
      "n-dimensional lipschitz graphs",
      "n-dimensional riesz transform"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 38,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1101.1734M"
    }
  }
}