{
  "id": "1311.1842",
  "version": "v1",
  "published": "2013-11-07T22:56:00.000Z",
  "updated": "2013-11-07T22:56:00.000Z",
  "title": "Extremal Domains for Self-Commutators in the Bergman Space",
  "authors": [
    "Matthew Fleeman",
    "Dmitry Khavinson"
  ],
  "comment": "10 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "In arXiv:1305.5193v1, the authors have shown that Putnam's inequality for the norm of self-commutators can be improved by a factor of $\\frac{1}{2}$ for Toeplitz operators with analytic symbol $\\varphi$ acting on the Bergman space $A^{2}(\\Omega)$. This improved upper bound is sharp when $\\varphi(\\Omega)$ is a disk. In this paper we show that disks are the only domains for which the upper bound is attained.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-11-07T22:56:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "bergman space",
      "extremal domains",
      "self-commutators",
      "upper bound",
      "toeplitz operators"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1311.1842F"
    }
  }
}