{
  "id": "0711.2868",
  "version": "v1",
  "published": "2007-11-19T09:10:01.000Z",
  "updated": "2007-11-19T09:10:01.000Z",
  "title": "Weighted Sobolev L2 estimates for a class of Fourier integral operators",
  "authors": [
    "Michael Ruzhansky",
    "Mitsuru Sugimoto"
  ],
  "comment": "27 pages",
  "journal": "Math. Nachr., 284 (2011), 1715-1738",
  "categories": [
    "math.AP",
    "math.FA"
  ],
  "abstract": "In this paper we develop elements of the global calculus of Fourier integral operators in $R^n$ under minimal decay assumptions on phases and amplitudes. We also establish global weighted Sobolev $L^2$ estimates for a class of Fourier integral operators that appears in the analysis of global smoothing problems for dispersive partial differential equations. As an application, we exhibit a new type of smoothing estimates for hyperbolic equations, where the decay of data in space is quantitatively translated into the time decay of solutions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-11-19T09:10:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35S30",
      "47G30",
      "35J10",
      "35G10",
      "35B65"
    ],
    "keywords": [
      "fourier integral operators",
      "weighted sobolev l2 estimates",
      "minimal decay assumptions",
      "dispersive partial differential equations",
      "time decay"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0711.2868R"
    }
  }
}