{
  "id": "math/0503723",
  "version": "v4",
  "published": "2005-03-31T03:23:09.000Z",
  "updated": "2005-12-27T15:13:13.000Z",
  "title": "The Essential Norm of Composition Operator between Generalized Bloch Spaces in Polydiscs and its Applications",
  "authors": [
    "Zehua Zhou",
    "Yan Liu"
  ],
  "comment": "24 Pages",
  "journal": "Jour nal of Inequalities and Application, 2006 (2006), Article ID 90742",
  "doi": "10.1155/JIA/2006/90742",
  "categories": [
    "math.FA",
    "math.CV"
  ],
  "abstract": "Let $U^{n}$ be the unit polydisc of ${\\Bbb C}^{n}$ and $\\phi=(\\phi_1, >..., \\phi_n)$ a holomorphic self-map of $U^{n}.$ By ${\\cal B}^p(U^{n})$, ${\\cal B}^p_{0}(U^{n})$ and ${\\cal B}^p_{0*}(U^{n})$ denote the $p$-Bloch space, Little $p$-Bloch space and Little star $p$-Bloch space in the unit polydisc $U^n$ respectively, where $p, q>0$. This paper gives the estimates of the essential norms of bounded composition operators $C_{\\phi}$ induced by $\\phi$ between ${\\cal B}^p(U^n)$ (${\\cal B}^p_{0}(U^n)$ or ${\\cal B}^p_{0*}(U^n)$) and ${\\cal B}^q(U^n)$ (${\\cal B}^q_{0}(U^n)$ or ${\\cal B}^q_{0*}(U^n)$). As their applications, some necessary and sufficient conditions for the bounded composition operators $C_{\\phi}$ to be compact from ${\\cal B}^p(U^n)$ $({\\cal B}^p_{0}(U^n)$ or ${\\cal B}^p_{0*}(U^n))$ into ${\\cal B}^q(U^n)$ (${\\cal B}^q_{0}(U^n)$ or ${\\cal B}^q_{0*}(U^n)$) are obtained.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2005-12-27T15:13:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47B38",
      "32A37",
      "47B33",
      "32A30"
    ],
    "keywords": [
      "generalized bloch spaces",
      "essential norm",
      "applications",
      "bounded composition operators",
      "unit polydisc"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......3723Z"
    }
  }
}