{
  "id": "1310.4268",
  "version": "v1",
  "published": "2013-10-16T04:31:53.000Z",
  "updated": "2013-10-16T04:31:53.000Z",
  "title": "Composition operators on generalized Hardy spaces",
  "authors": [
    "Sam Elliott",
    "Juliette Leblond",
    "Elodie Pozzi",
    "Emmanuel Russ"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "Let $\\Omega_1,\\Omega_2\\subset {\\mathbb C}$ be bounded domains. Let $\\phi:\\Omega_1\\rightarrow \\Omega_2$ holomorphic in $\\Omega_1$ and belonging to $W^{1,\\infty}_{\\Omega_2}(\\Omega_1)$. We study the composition operators $f\\mapsto f\\circ\\phi$ on generalized Hardy spaces on $\\Omega_2$, recently considered in \\cite{bfl, BLRR}. In particular, we provide necessary and/or sufficient conditions on $\\phi$, depending on the geometry of the domains, ensuring that these operators are bounded, invertible, isometric or compact. Some of our results are new even for Hardy spaces of analytic functions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-10-16T04:31:53.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "generalized hardy spaces",
      "composition operators",
      "sufficient conditions",
      "analytic functions",
      "bounded domains"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1310.4268E"
    }
  }
}