{
  "id": "1309.5016",
  "version": "v3",
  "published": "2013-09-19T15:20:45.000Z",
  "updated": "2013-11-02T13:27:45.000Z",
  "title": "The associated weight and the essential norm of weighted composition operators",
  "authors": [
    "María T. Malavé Ramírez",
    "Julio C. Ramos Fernández"
  ],
  "comment": "This paper has been withdrawn by the author due to Major Revisions is requested",
  "categories": [
    "math.FA"
  ],
  "abstract": "For an almost radial and typical weight $v$, we characterize the continuity and compactness of the weighted composition operator $u C_{\\varphi}$ acting on the weighted Banach spaces of analytic functions $H_{v}^{\\infty}$ in terms of the $n$th power of the symbol $\\varphi$, where $u: \\mathbb{D} \\to \\mathbb{C}$ is an analytic function and $\\varphi: \\mathbb{D} \\to \\mathbb{D}$ is analytic. More precisely, we extend the results of Hyv\\\"arinen, Kemppainen, Lindstr\\\"om, Rautio and Saukko relating to the continuity and essential norm calculus of the operator $u C_{\\varphi}$.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2013-11-02T13:27:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46B33",
      "47B38",
      "30H30"
    ],
    "keywords": [
      "weighted composition operator",
      "associated weight",
      "analytic function",
      "essential norm calculus",
      "continuity"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1309.5016M"
    }
  }
}