{
  "id": "1708.01326",
  "version": "v1",
  "published": "2017-08-03T22:46:36.000Z",
  "updated": "2017-08-03T22:46:36.000Z",
  "title": "On bilinear Hilbert transform along two polynomials",
  "authors": [
    "Dong Dong"
  ],
  "comment": "submitted",
  "categories": [
    "math.CA"
  ],
  "abstract": "We prove that the bilinear Hilbert transform along two polynomials $B_{P,Q}(f,g)(x)=\\int_{\\mathbb{R}}f(x-P(t))g(x-Q(t))\\frac{dt}{t}$ is bounded from $L^p \\times L^q$ to $L^r$ for a large range of $(p,q,r)$, as long as the polynomials $P$ and $Q$ have distinct leading and trailing degrees. The same boundedness property holds for the corresponding bilinear maximal function $\\mathcal{M}_{P,Q}(f,g)(x)=\\sup_{\\epsilon>0}\\frac{1}{2\\epsilon}\\int_{-\\epsilon}^{\\epsilon} |f(x-P(t))g(x-Q(t))|dt$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-08-03T22:46:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B20",
      "47B38"
    ],
    "keywords": [
      "bilinear hilbert transform",
      "polynomials",
      "boundedness property holds",
      "corresponding bilinear maximal function",
      "large range"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}