{
  "id": "1811.05209",
  "version": "v1",
  "published": "2018-11-13T11:00:15.000Z",
  "updated": "2018-11-13T11:00:15.000Z",
  "title": "Quantitative $C_p$ estimates for Calderón-Zygmund operators",
  "authors": [
    "Javier Canto"
  ],
  "categories": [
    "math.CA"
  ],
  "abstract": "We prove an appropriate quantitative reverse H\\\"older inequality for the $C_p$ class of weights from which we obtain as a limiting case the sharp reverse H\\\"older inequality for the $A_\\infty$ class of weights. We use this result to provide a quantitative weighted norm inequality between Calder\\'on-Zygmund operators and the Hardy-Littlewood maximal function, precisely $$||Tf||_{L^p(w)} \\lesssim_{T,n,p,q} [w]_{C_q}(1+\\log^+[w]_{C_q})||Mf||_{L^p(w)},$$ for $w\\in C_q$ and $q>p>1$ improving Sawyer's theorem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-11-13T11:00:15.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "calderón-zygmund operators",
      "hardy-littlewood maximal function",
      "improving sawyers theorem",
      "quantitative weighted norm inequality",
      "sharp reverse"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}