{
  "id": "0902.2742",
  "version": "v1",
  "published": "2009-02-16T17:09:15.000Z",
  "updated": "2009-02-16T17:09:15.000Z",
  "title": "Subharmonicity of higher dimensional exponential transforms",
  "authors": [
    "Vladimir Tkachev"
  ],
  "comment": "21 pages",
  "journal": "Oper. Theory Adv. Appl., V.156, Birkhauser, 2005, 257--277",
  "doi": "10.1007/3-7643-7316-4_13",
  "categories": [
    "math.FA",
    "math.AP"
  ],
  "abstract": "Our main result is an extension of the classical Cauchy inequality for the case of bounded densities. In particular, this implies subharmonicity of the function $M_n(E)$, where $V_n(x)$ is the critical Riesz potential in $R^n$ ($\\alpha=n$) of a density $0\\leq \\rho\\leq 1$ and $M_n(t)$ is the profile function: the solution of $y'(t)=1-y^{n/2}(t)$, $y(0)=0$. We show thath this result is optimal (in the sense that $M_n(E)$ is harmnoic for characteristic functions of a ball) and give thereby an affirmative answer to one question posed by B. Gustafsson and M. Putinar (Ind. Univ. Math. J., 52(2003), 527-568).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-02-16T17:09:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "31C05",
      "31B15",
      "44A12"
    ],
    "keywords": [
      "higher dimensional exponential transforms",
      "main result",
      "characteristic functions",
      "classical cauchy inequality",
      "critical riesz potential"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0902.2742T"
    }
  }
}