{
  "id": "1612.03958",
  "version": "v1",
  "published": "2016-12-12T22:42:20.000Z",
  "updated": "2016-12-12T22:42:20.000Z",
  "title": "On weak weighted estimates of martingale transform",
  "authors": [
    "Fedor Nazarov",
    "Alexander Reznikov",
    "Vasily Vasyunin",
    "Alexander Volberg"
  ],
  "comment": "25 pages",
  "categories": [
    "math.AP",
    "math.CA",
    "math.FA"
  ],
  "abstract": "We consider several weak type estimates for singular operators using the Bellman function approach. We disprove the $A_1$ conjecture of Muckenhoupt, which stayed open after Muckenhoupt--Wheeden's conjecture was disproved by Reguera--Thiele.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-12-12T22:42:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B20",
      "42B35",
      "47A30",
      "F.2.2"
    ],
    "keywords": [
      "weak weighted estimates",
      "martingale transform",
      "weak type estimates",
      "bellman function approach",
      "singular operators"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}