{
  "id": "1011.5763",
  "version": "v1",
  "published": "2010-11-26T11:32:56.000Z",
  "updated": "2010-11-26T11:32:56.000Z",
  "title": "The boundedness of some operators with rough kernel on the weighted Morrey spaces",
  "authors": [
    "Hua Wang"
  ],
  "comment": "17 pages",
  "categories": [
    "math.CA"
  ],
  "abstract": "Let $\\Omega\\in L^q(S^{n-1})$ with $1<q\\le\\infty$ be homogeneous of degree zero and has mean value zero on $S^{n-1}$. In this paper, we will study the boundedness of homogeneous singular integrals and Marcinkiewicz integrals with rough kernel on the weighted Morrey spaces $L^{p,\\kappa}(w)$ for $q'\\le p<\\infty$(or $q'<p<\\infty$) and $0<\\kappa<1$. We will also prove that the commutator operators formed by a $BMO(\\mathbb R^n)$ function $b(x)$ and these rough operators are bounded on the weighted Morrey spaces $L^{p,\\kappa}(w)$ for $q'<p<\\infty$ and $0<\\kappa<1$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-11-26T11:32:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B20",
      "42B25",
      "42B35"
    ],
    "keywords": [
      "weighted morrey spaces",
      "rough kernel",
      "boundedness",
      "mean value zero",
      "homogeneous singular integrals"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1011.5763W"
    }
  }
}