{
  "id": "1610.00444",
  "version": "v1",
  "published": "2016-10-03T08:48:39.000Z",
  "updated": "2016-10-03T08:48:39.000Z",
  "title": "Sharp weighted estimates for multi-frequency Calderón-Zygmund operators",
  "authors": [
    "Saurabh Shrivastava",
    "Senthil Raani K. S"
  ],
  "categories": [
    "math.CA"
  ],
  "abstract": "In this paper we study weighted estimates for the multi-frequency $\\omega-$Calder\\'on-Zygmund operators $T$ associated with the frequency set $\\Theta=\\{\\xi_1,\\xi_2,\\dots,\\xi_N\\}$ and modulus of continuity $\\omega$ satisfying the usual Dini condition. We use the modern method of domination by sparse operators and obtain sharp bounds $\\|T\\|_{L^p(w)\\rightarrow L^p(w)}\\lesssim N^{\\frac{1}{2}}[w]_{\\mathbb{A}_p}^{max(1,\\frac{1}{p-1})}$ for the exponents of $N$ and $\\mathbb{A}_p$ characteristic $[w]_{\\mathbb{A}_p}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-10-03T08:48:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B20",
      "42B25"
    ],
    "keywords": [
      "multi-frequency calderón-zygmund operators",
      "sharp weighted estimates",
      "usual dini condition",
      "frequency set",
      "sharp bounds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}