{
  "id": "1602.08208",
  "version": "v1",
  "published": "2016-02-26T06:08:52.000Z",
  "updated": "2016-02-26T06:08:52.000Z",
  "title": "$L^p$-mapping properties for Schrödinger operators in open sets of $\\mathbb R ^d$",
  "authors": [
    "T. Iwabuchi",
    "T. Matsuyama",
    "K. Taniguchi"
  ],
  "comment": "32 pages",
  "categories": [
    "math.FA",
    "math.SP"
  ],
  "abstract": "Let $H_V=-\\Delta +V$ be a Schr\\\"odinger operator on an arbitrary open set $\\Omega$ of $\\mathbb R^d$, where $d \\geq 3$, and $\\Delta$ is the Dirichlet Laplacian and the potential $V$ belongs to the Kato class on $\\Omega$. The purpose of this paper is to show $L^p$-boundedness of an operator $\\varphi(H_V)$ for any rapidly decreasing function $\\varphi$ on $\\mathbb R$. $\\varphi(H_V)$ is defined by the spectral theorem. As a by-product, $L^p$-$L^q$-estimates for $\\varphi(H_V)$ are also obtained.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-02-26T06:08:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47F05",
      "26D10"
    ],
    "keywords": [
      "schrödinger operators",
      "mapping properties",
      "arbitrary open set",
      "dirichlet laplacian",
      "kato class"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160208208I"
    }
  }
}