{
  "id": "1110.3517",
  "version": "v2",
  "published": "2011-10-16T19:11:31.000Z",
  "updated": "2015-12-31T23:26:20.000Z",
  "title": "On the Boundedness of The Bilinear Hilbert Transform along \"non-flat\" smooth curves",
  "authors": [
    "Victor Lie"
  ],
  "comment": "48 pages, no figures. Published in Amer. J. Math., 137(2), pp. 313-364, 2015",
  "categories": [
    "math.CA"
  ],
  "abstract": "We are proving $L^2(\\R)\\times L^2(\\R)\\,\\rightarrow\\,L^1(\\R)$ bounds for the bilinear Hilbert transform $H_{\\Gamma}$ along curves $\\Gamma=(t,-\\gamma(t))$ with $\\gamma$ being a smooth \"non-flat\" curve near zero and infinity.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-10-16T19:11:31.000Z",
      "abstract": "We are proving $L^2(\\R)\\times L^2(\\R)\\,\\rightarrow\\,L^1(\\R)$ bounds for the bilinear Hilbert transform $H_{\\G}$ along curves $\\Gamma=(t,-\\gamma(t))$ with $\\g$ being a smooth \"non-flat\" curve near zero and infinity.",
      "comment": "31 pages, no figures",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2015-12-31T23:26:20.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "bilinear hilbert transform",
      "smooth curves",
      "boundedness"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 48,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1110.3517L"
    }
  }
}