{
  "id": "2009.02456",
  "version": "v1",
  "published": "2020-09-05T04:33:15.000Z",
  "updated": "2020-09-05T04:33:15.000Z",
  "title": "Sparse domination and weighted estimates for rough bilinear singular integrals",
  "authors": [
    "Loukas Grafakos",
    "Zhidan Wang",
    "Qingying Xue"
  ],
  "comment": "22 pages",
  "categories": [
    "math.CA"
  ],
  "abstract": "Let $r>\\frac{4}{3}$ and let $\\Omega \\in L^{r}(\\mathbb{S}^{2n-1})$ have vanishing integral. We show that the bilinear rough singular integral $$T_{\\Omega}(f,g)(x)= \\textrm{p.v.} \\int_{\\mathbb{R}^n}\\int_{\\mathbb{R}^n}\\frac{\\Omega((y,z)/|(y,z)|)}{|(y,z)|^{2n}}f(x-y)g(x-z)\\,dydz,$$ satisfies a sparse bound by $(p,p,p)$-averages, where $p$ is bigger than a certain number explicitly related to $r$ and $n$. As a consequence we deduce certain quantitative weighted estimates for bilinear homogeneous singular integrals associated with rough homogeneous kernels.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-09-05T04:33:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B20"
    ],
    "keywords": [
      "rough bilinear singular integrals",
      "weighted estimates",
      "sparse domination",
      "bilinear rough singular integral",
      "bilinear homogeneous singular integrals"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}