{
  "id": "math/0311219",
  "version": "v1",
  "published": "2003-11-13T16:52:51.000Z",
  "updated": "2003-11-13T16:52:51.000Z",
  "title": "Global L2-boundedness theorems for a class of Fourier integral operators",
  "authors": [
    "Michael Ruzhansky",
    "Mitsuru Sugimoto"
  ],
  "journal": "Comm. Partial Differential Equations, 31 (2006), 547-569.",
  "categories": [
    "math.AP",
    "math.FA"
  ],
  "abstract": "The local $L^2$-mapping property of Fourier integral operators has been established in H\\\"ormander \\cite{H} and in Eskin \\cite{E}. In this paper, we treat the global $L^2$-boundedness for a class of operators that appears naturally in many problems. As a consequence, we will improve known global results for several classes of pseudo-differential and Fourier integral operators, as well as extend previous results of Asada and Fujiwara \\cite{AF} or Kumano-go \\cite{Ku}. As an application, we show a global smoothing estimate to generalized Schr\\\"odinger equations which extends the results of Ben-Artzi and Devinatz \\cite{BD}, Walther \\cite{Wa}, and \\cite{Wa2}.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2003-11-13T16:52:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35S30"
    ],
    "keywords": [
      "fourier integral operators",
      "global l2-boundedness theorems",
      "global results",
      "global smoothing estimate",
      "consequence"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math.....11219R"
    }
  }
}