{
  "id": "0910.2751",
  "version": "v1",
  "published": "2009-10-14T23:56:46.000Z",
  "updated": "2009-10-14T23:56:46.000Z",
  "title": "Global Lp continuity of Fourier integral operators",
  "authors": [
    "Sandro Coriasco",
    "Michael Ruzhansky"
  ],
  "comment": "20 pages",
  "categories": [
    "math.FA",
    "math.AP"
  ],
  "abstract": "In this paper we establish global Lp regularity properties of Fourier integral operators. The orders of decay of the amplitude are determined for operators to be bounded on $L^p(\\Rn)$, $1<p<\\infty$, as well as to be bounded from Hardy space $H^1(\\Rn)$ to $L^1(\\Rn)$. The obtained results extend local $L^p$ regularity properties of Fourier integral operators established by Seeger, Sogge and Stein (1991) as well as global $L^2(\\Rn)$ results of Asada and Fujiwara (1978) and Ruzhansky and Sugimoto (2006), to the global setting of $L^p(\\Rn)$. Global boundedness in weighted Sobolev spaces $W^{\\sigma,p}_s(\\Rn)$ is also established. The techniques used in the proofs are the space dependent dyadic decomposition and the global calculi developed by Ruzhansky and Sugimoto (2006) and Coriasco (1999).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-10-14T23:56:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35S30",
      "42B30",
      "46E30",
      "47B34"
    ],
    "keywords": [
      "fourier integral operators",
      "global lp continuity",
      "space dependent dyadic decomposition",
      "establish global lp regularity properties",
      "results extend local"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0910.2751C"
    }
  }
}