{
  "id": "1301.4663",
  "version": "v5",
  "published": "2013-01-20T14:44:44.000Z",
  "updated": "2014-03-01T23:35:27.000Z",
  "title": "Two Weight Inequality for the Hilbert Transform: A Real Variable Characterization, II",
  "authors": [
    "Michael T Lacey"
  ],
  "comment": "Final Version, to appear in Duke",
  "categories": [
    "math.CA",
    "math.CV"
  ],
  "abstract": "A conjecture of Nazarov--Treil--Volberg on the two weight inequality for the Hilbert transform is verified. Given two non-negative Borel measures u and w on the real line, the Hilbert transform $H_u$ maps $L^2(u)$ to $L^2(w)$ if and only if the pair of measures of satisfy a Poisson $A_2$ condition, and dual collections of testing conditions, uniformly over all intervals. This strengthens a prior characterization of Lacey-Sawyer-Shen-Uriate-Tuero arxiv:1201.4319. The latter paper includes a `Global to Local' reduction. This article solves the Local problem.",
  "revisions": [
    {
      "version": "v5",
      "updated": "2014-03-01T23:35:27.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hilbert transform",
      "real variable characterization",
      "weight inequality",
      "non-negative borel measures",
      "real line"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1301.4663L"
    }
  }
}