{
  "id": "math-ph/0605036",
  "version": "v1",
  "published": "2006-05-10T13:40:30.000Z",
  "updated": "2006-05-10T13:40:30.000Z",
  "title": "The $L^p$ boundedness of wave operators for Schrödinger operators with threshold singularities II. Even dimensional case",
  "authors": [
    "Domenico Finco",
    "Kenji Yajima"
  ],
  "comment": "59 pages",
  "categories": [
    "math-ph",
    "math.MP",
    "math.SP"
  ],
  "abstract": "In this paper we consider the wave operators $W_{\\pm}$ for a Schr\\\"odinger operator $H$ in ${\\bf{R}}^n$ with $n\\geq 4$ even and we discuss the $L^p$ boundedness of $W_{\\pm}$ assuming a suitable decay at infinity of the potential $V$. The analysis heavily depends on the singularities of the resolvent for small energy, that is if 0-energy eigenstates exist. If such eigenstates do not exist $W_{\\pm}: L^p \\to L^p$ are bounded for $1 \\leq p \\leq \\infty$ otherwise this is true for $ \\frac{n}{n-2} < p < \\frac{n}{2} $. The extension to Sobolev space is discussed.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-05-10T13:40:30.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "wave operators",
      "dimensional case",
      "schrödinger operators",
      "threshold singularities",
      "boundedness"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 59,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math.ph...5036F"
    }
  }
}