{
  "id": "0807.0246",
  "version": "v8",
  "published": "2008-07-01T21:47:46.000Z",
  "updated": "2011-02-03T01:48:12.000Z",
  "title": "A characterization of two weight norm inequalities for maximal singular integrals with one doubling measure",
  "authors": [
    "M. T. Lacey",
    "E. T. Sawyer",
    "I. Uriarte-Tuero"
  ],
  "comment": "64 pages. Submitted to A&PDE. Minor revisions, based on a final referees report",
  "categories": [
    "math.CA"
  ],
  "abstract": "We characterize two-weight inequalities for certain maximal truncations of the Hilbert transform in terms of testing conditions on simpler functions. For 1<p<2 and two positive Borel measures u, v on R, we assume that u is doubling, and we consider maximal truncations T_# of the Hilbert transform. The norm estimate || T(f u) ||_{L^p(v)} < C || f ||_{L^p(u)} is characterized in terms of an A_p condition on the weights and two testing conditions. The first is the norm condition above, but the function f varies over bounded functions supported on a cube. The second is a dual weak-type condition, for arbitrary functions. This result should be compared to the result of Nazarov, Treil and Volberg, arXiv:math/0702758. Additional results are obtained for 2<p<\\infty, and for the weak type inequality.",
  "revisions": [
    {
      "version": "v8",
      "updated": "2011-02-03T01:48:12.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "weight norm inequalities",
      "maximal singular integrals",
      "doubling measure",
      "characterization",
      "hilbert transform"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 64,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0807.0246L"
    }
  }
}