{
  "id": "math-ph/0509059",
  "version": "v3",
  "published": "2005-09-26T17:58:59.000Z",
  "updated": "2005-09-29T09:11:40.000Z",
  "title": "L^p boundedness of the wave operator for the one dimensional Schroedinger operator",
  "authors": [
    "Piero D'Ancona",
    "Luca Fanelli"
  ],
  "comment": "26 pages",
  "doi": "10.1007/s00220-006-0098-x",
  "categories": [
    "math-ph",
    "math.AP",
    "math.MP"
  ],
  "abstract": "Given a one dimensional perturbed Schroedinger operator H=-(d/dx)^2+V(x) we consider the associated wave operators W_+, W_- defined as the strong L^2 limits as s-> \\pm\\infty of the operators e^{isH} e^{-isH_0} We prove that the wave operators are bounded operators on L^p for all 1<p<\\infty, provided (1+|x|)^2 V(x) is integrable, or else (1+|x|)V(x) is integrable and 0 is not a resonance. For p=\\infty we obtain an estimate in terms of the Hilbert transform. Some applications to dispersive estimates for equations with variable rough coefficients are given.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2005-09-29T09:11:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "58J50"
    ],
    "keywords": [
      "dimensional schroedinger operator",
      "boundedness",
      "dimensional perturbed schroedinger operator",
      "associated wave operators",
      "hilbert transform"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Springer",
      "journal": "Commun. Math. Phys."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}