{
  "id": "0804.3928",
  "version": "v1",
  "published": "2008-04-24T13:53:34.000Z",
  "updated": "2008-04-24T13:53:34.000Z",
  "title": "On the global boundedness of Fourier integral operators",
  "authors": [
    "Elena Cordero",
    "Fabio Nicola",
    "Luigi Rodino"
  ],
  "comment": "30 pages",
  "categories": [
    "math.FA",
    "math.AP"
  ],
  "abstract": "We consider a class of Fourier integral operators, globally defined on $\\mathbb{R}^{d}$, with symbols and phases satisfying product type estimates (the so-called $SG$ or scattering classes). We prove a sharp continuity result for such operators when acting on the modulation spaces $M^p$. The minimal loss of derivatives is shown to be $d|1/2-1/p|$. This global perspective produces a loss of decay as well, given by the same order. Strictly related, striking examples of unboundedness on $L^p$ spaces are presented.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-04-24T13:53:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35S30",
      "47G30",
      "42C15"
    ],
    "keywords": [
      "fourier integral operators",
      "global boundedness",
      "phases satisfying product type estimates",
      "sharp continuity result",
      "global perspective produces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0804.3928C"
    }
  }
}