{
  "id": "0801.1444",
  "version": "v3",
  "published": "2008-01-09T14:34:50.000Z",
  "updated": "2008-04-24T10:49:25.000Z",
  "title": "Boundedness of Fourier Integral Operators on $\\mathcal{F} L^p$ spaces",
  "authors": [
    "Elena Cordero",
    "Fabio Nicola",
    "Luigi Rodino"
  ],
  "comment": "26 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We study the action of Fourier Integral Operators (FIOs) of H{\\\"o}rmander's type on ${\\mathcal{F}} L^p({\\mathbb {R}}^d_{comp}$, $1\\leq p\\leq\\infty$. We see, from the Beurling-Helson theorem, that generally FIOs of order zero fail to be bounded on these spaces when $p\\not=2$, the counterexample being given by any smooth non-linear change of variable. Here we show that FIOs of order $m=-d|1/2-1/p|$ are instead bounded. Moreover, this loss of derivatives is proved to be sharp in every dimension $d\\geq1$, even for phases which are linear in the dual variables. The proofs make use of tools from time-frequency analysis such as the theory of modulation spaces.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2008-04-24T10:49:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35S30",
      "47G30",
      "42C15"
    ],
    "keywords": [
      "fourier integral operators",
      "boundedness",
      "smooth non-linear change",
      "order zero fail",
      "time-frequency analysis"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0801.1444C"
    }
  }
}