{
  "id": "1709.03123",
  "version": "v1",
  "published": "2017-09-10T16:26:10.000Z",
  "updated": "2017-09-10T16:26:10.000Z",
  "title": "Weighted jump and variational inequalities for rough operators",
  "authors": [
    "Yanping Chen",
    "Yong Ding",
    "Guixiang Hong",
    "Honghai Liu"
  ],
  "comment": "28 pages",
  "categories": [
    "math.CA"
  ],
  "abstract": "In this paper, we systematically study weighted jump and variational inequalities for rough operators. More precisely, we show some weighted jump and variational inequalities for the families $\\mathcal T:=\\{T_\\varepsilon\\}_{\\varepsilon>0}$ of truncated singular integrals and $\\mathcal M_{\\Omega}:=\\{M_{\\Omega,t}\\}_{t>0}$ of averaging operators with rough kernels, which are defined respectively by $$ T_\\varepsilon f(x)=\\int_{|y|>\\varepsilon}\\frac{\\Omega(y')}{|y|^n}f(x-y)dy$$ and $$M_{\\Omega,t} f(x)=\\frac1{t^n}\\int_{|y|<t}\\Omega(y')f(x-y)dy, $$ where the kernel $\\Omega$ belongs to $L^q(\\mathbf S^{n-1})$ for $q>1$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-09-10T16:26:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B20",
      "42B25"
    ],
    "keywords": [
      "variational inequalities",
      "rough operators",
      "truncated singular integrals",
      "rough kernels",
      "systematically study weighted jump"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}