{
  "id": "0807.2380",
  "version": "v2",
  "published": "2008-07-15T14:16:23.000Z",
  "updated": "2009-08-28T14:54:02.000Z",
  "title": "Boundedness of Schroedinger type propagators on modulation spaces",
  "authors": [
    "Elena Cordero",
    "Fabio Nicola"
  ],
  "comment": "30 pages",
  "categories": [
    "math.FA",
    "math.AP"
  ],
  "abstract": "It is known that Fourier integral operators arising when solving Schr\\\"odinger-type operators are bounded on the modulation spaces $\\cM^{p,q}$, for $1\\leq p=q\\leq\\infty$, provided their symbols belong to the Sj\\\"ostrand class $M^{\\infty,1}$. However, they generally fail to be bounded on $\\cM^{p,q}$ for $p\\not=q$. In this paper we study several additional conditions, to be imposed on the phase or on the symbol, which guarantee the boundedness on $\\cM^{p,q}$ for $p\\not=q$, and between $\\cM^{p,q}\\to\\cM^{q,p}$, $1\\leq q< p\\leq\\infty$. We also study similar problems for operators acting on Wiener amalgam spaces, recapturing, in particular, some recent results for metaplectic operators. Our arguments make heavily use of the uncertainty principle.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-08-28T14:54:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35S30",
      "47G30"
    ],
    "keywords": [
      "schroedinger type propagators",
      "modulation spaces",
      "boundedness",
      "wiener amalgam spaces",
      "study similar problems"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0807.2380C"
    }
  }
}