{
  "id": "0709.1431",
  "version": "v1",
  "published": "2007-09-10T16:13:00.000Z",
  "updated": "2007-09-10T16:13:00.000Z",
  "title": "Essential Norms of Weighted Composition Operators between Hardy Spaces in the unit Ball",
  "authors": [
    "Zhong-Shan Fang",
    "Ze-Hua Zhou"
  ],
  "comment": "17 pages",
  "journal": "Journal of Applied Functional Analysis, 5(3)( 2010), 251-265",
  "categories": [
    "math.FA",
    "math.CV"
  ],
  "abstract": "Let $\\phi(z)=(\\phi_1(z),...,\\phi_n(z))$ be a holomorphic self-map of $B_n$ and $\\psi(z)$ a holomorphic function on $B_n$, and $H(B_n)$ the class of all holomorphic functions on $B_n$, where $B_n$ is the unit ball of $C^n$, the weight composition operator $W_{\\psi,\\phi}$ is defined by $W_{\\psi,\\phi}=\\psi f(\\phi)$ for $f\\in H(B_n)$. In this paper we estimate the essential norm for the weighted composition operator $W_{\\psi,\\phi}$ acting from the Hardy space $H^p$ to $H^q$ ($0<p,q\\leq \\infty$). When $p=\\infty$ and $q=2$, we give an exact formula for the essential norm. As their applications, we also obtain some sufficient and necessary conditions for the bounded weighted composition operator to be compact from $H^p$ to $H^q$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-09-10T16:13:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47B38",
      "47B33",
      "26A16",
      "32A16",
      "32A37"
    ],
    "keywords": [
      "essential norm",
      "unit ball",
      "hardy space",
      "holomorphic function",
      "weight composition operator"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0709.1431F"
    }
  }
}