{
  "id": "1801.05275",
  "version": "v1",
  "published": "2018-01-10T01:15:09.000Z",
  "updated": "2018-01-10T01:15:09.000Z",
  "title": "Two-weight, weak type norm inequalities for fractional integral operators and commutators on weighted Morrey and amalgam spaces",
  "authors": [
    "Hua Wang"
  ],
  "comment": "32 pages",
  "categories": [
    "math.CA"
  ],
  "abstract": "Let $0<\\gamma<n$ and $I_\\gamma$ be the fractional integral operator of order $\\gamma$, $I_{\\gamma}f(x)=\\int_{\\mathbb R^n}|x-y|^{\\gamma-n}f(y)\\,dy$, and let $[b,I_\\gamma]$ be the linear commutator generated by a symbol function $b$ and $I_\\gamma$, $[b,I_{\\gamma}]f(x)=b(x)\\cdot I_{\\gamma}f(x)-I_\\gamma(bf)(x)$. This paper is concerned with two-weight, weak type norm estimates for such operators on the weighted Morrey and amalgam spaces. Based on weak-type norm inequalities on weighted Lebesgue spaces and certain $A_p$-type conditions on pairs of weights, we can establish the weak-type norm inequalities for fractional integral operator $I_{\\gamma}$ as well as the corresponding commutator in the framework of weighted Morrey and amalgam spaces. Furthermore, some estimates for the extreme case are also obtained on these weighted spaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-01-10T01:15:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B20",
      "46E30",
      "47B38",
      "47G10"
    ],
    "keywords": [
      "fractional integral operator",
      "weak type norm inequalities",
      "amalgam spaces",
      "weighted morrey",
      "commutator"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}