{
  "id": "0709.1435",
  "version": "v1",
  "published": "2007-09-10T16:20:46.000Z",
  "updated": "2007-09-10T16:20:46.000Z",
  "title": "Composition operators in the Lipschitz Space of the Polydiscs",
  "authors": [
    "Zhongshan Fang",
    "Zehua Zhou"
  ],
  "comment": "7 pages",
  "journal": "J. Comput. Anal. Appl. 12 (1-B) (2010) , 222-227",
  "categories": [
    "math.FA",
    "math.CV"
  ],
  "abstract": "In 1987, Shapiro shew that composition operator induced by symbol $\\phi$ is compact on the Lipschltz space if and only if the infinity norm of $\\phi$ is less than 1 by a spectral-theoretic argument, where $\\phi$ is a holomorphic self-map of the unit disk. In this paper, we shall generalize Shapiro's result to the $n$-dimensional case.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-09-10T16:20:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47B38",
      "47B33",
      "32A16",
      "32A26",
      "32A37"
    ],
    "keywords": [
      "composition operator",
      "lipschitz space",
      "shapiro shew",
      "infinity norm",
      "dimensional case"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0709.1435F"
    }
  }
}