{
  "id": "1108.2319",
  "version": "v1",
  "published": "2011-08-11T01:46:53.000Z",
  "updated": "2011-08-11T01:46:53.000Z",
  "title": "The Two Weight Inequality for Hilbert Transform, Coronas, and Energy Conditions",
  "authors": [
    "Michael T. Lacey",
    "Eric T. Sawyer",
    "Chun-Yen Shen",
    "Ignacio Uriarte-Tuero"
  ],
  "comment": "24 pages, 1 figure",
  "categories": [
    "math.CA"
  ],
  "abstract": "We consider the two weight problem for the Hilbert transform, namely the question of finding real-variable characterization of those pair of weights for which the Hilbert transform acts boundedly on $ L ^2 $ of the weights. Such a characterization is known subject to certain side conditions. We give a new proof, simpler in many details, of the best such result. In addition, we analyze underlying assumptions in the proof, especially in terms of two alternate side conditions. A new characterization in the case of one doubling weight is given.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-08-11T01:46:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B20",
      "42B25",
      "42B35"
    ],
    "keywords": [
      "weight inequality",
      "energy conditions",
      "alternate side conditions",
      "characterization",
      "hilbert transform acts"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1108.2319L"
    }
  }
}