{
  "id": "0805.4122",
  "version": "v1",
  "published": "2008-05-27T13:53:17.000Z",
  "updated": "2008-05-27T13:53:17.000Z",
  "title": "Boundedness of Fourier integral operators on Fourier Lebesgue spaces and affine fibrations",
  "authors": [
    "Fabio Nicola"
  ],
  "comment": "13 pages",
  "categories": [
    "math.FA",
    "math.AP"
  ],
  "abstract": "We carry on the study of Fourier integral operators of H{\\\"o}rmander's type acting on the spaces $(\\mathcal{F}L^p)_{comp}$, $1\\leq p\\leq\\infty$, of compactly supported distributions whose Fourier transform is in $L^p$. We show that the sharp loss of derivatives for such an operator to be bounded on these spaces is related to the rank $r$ of the Hessian of the phase $\\Phi(x,\\eta)$ with respect to the space variables $x$. Indeed, we show that operators of order $m=-r|1/2-1/p|$ are bounded on $(\\mathcal{F}L^p)_{comp}$, if the mapping $x\\longmapsto\\nabla_x\\Phi(x,\\eta)$ is constant on the fibers, of codimension $r$, of an affine fibration.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-05-27T13:53:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35S30",
      "42B35"
    ],
    "keywords": [
      "fourier integral operators",
      "fourier lebesgue spaces",
      "affine fibration",
      "boundedness",
      "fourier transform"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0805.4122N"
    }
  }
}