{
  "id": "1206.2489",
  "version": "v1",
  "published": "2012-06-12T11:14:52.000Z",
  "updated": "2012-06-12T11:14:52.000Z",
  "title": "A simple proof of the sharp weighted estimate for Calderon-Zygmund operators on homogeneous spaces",
  "authors": [
    "Theresa C. Anderson",
    "Armen Vagharshakyan"
  ],
  "categories": [
    "math.CA"
  ],
  "abstract": "Here we show that Lerner's method of local mean oscillation gives a simple proof of the $A_2$ conjecture for spaces of homogeneous type: that is, the linear dependence on the $A_2$ norm for weighted $L^2$ Calderon-Zygmund operator estimates. In the Euclidean case, the result is due to Hyt\\\"{o}nen, and for geometrically doubling spaces, Nazarov, Rezinikov, and Volberg obtained the linear bound.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-06-12T11:14:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B20"
    ],
    "keywords": [
      "sharp weighted estimate",
      "simple proof",
      "homogeneous spaces",
      "local mean oscillation",
      "calderon-zygmund operator estimates"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1206.2489A"
    }
  }
}