{
  "id": "2003.12878",
  "version": "v1",
  "published": "2020-03-28T19:50:40.000Z",
  "updated": "2020-03-28T19:50:40.000Z",
  "title": "Regularity of Fourier integral operators with amplitudes in general Hörmander classes",
  "authors": [
    "Alejandro J. Castro",
    "Anders Israelsson",
    "Wolfgang Staubach"
  ],
  "comment": "41 pages",
  "categories": [
    "math.AP",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We prove the global $L^p$-boundedness of Fourier integral operators that model the parametrices for hyperbolic partial differential equations, with amplitudes in classical H\\\"ormander classes $S^{m}_{\\rho, \\delta}(\\mathbb{R}^n)$ for parameters $0<\\rho\\leq 1$, $0\\leq \\delta<1$. We also consider the regularity of operators with amplitudes in the exotic class $S^{m}_{0, \\delta}(\\mathbb{R}^n)$, $0\\leq \\delta< 1$ and the forbidden class $S^{m}_{\\rho, 1}(\\mathbb{R}^n)$, $0\\leq\\rho\\leq 1.$ Furthermore we show that despite the failure of the $L^2$-boundedness of operators with amplitudes in the forbidden class $S^{0}_{1, 1}(\\mathbb{R}^n)$, the operators in question are bounded on Sobolev spaces $H^s(\\mathbb{R}^n)$ with $s>0.$ This result extends those of Y. Meyer and E. M. Stein to the setting of Fourier integral operators.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-03-28T19:50:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B20",
      "47D06"
    ],
    "keywords": [
      "fourier integral operators",
      "general hörmander classes",
      "amplitudes",
      "regularity",
      "hyperbolic partial differential equations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 41,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}