{
  "id": "2302.00312",
  "version": "v1",
  "published": "2023-02-01T08:41:09.000Z",
  "updated": "2023-02-01T08:41:09.000Z",
  "title": "Boundedness of Fourier integral operators on classical function spaces",
  "authors": [
    "Anders Israelsson",
    "Tobias Mattsson",
    "Wolfgang Staubach"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We investigate the global boundedness of Fourier integral operators with amplitudes in the general H\\\"ormander classes $S^{m}_{\\rho, \\delta}(\\mathbb{R}^n)$, $\\rho, \\delta\\in [0,1]$ and non-degenerate phase functions of arbitrary rank $\\kappa\\in \\{0,1,\\dots, n-1\\}$ on Besov-Lipschitz $B^{s}_{p,q}(\\mathbb{R}^n)$ and Triebel-Lizorkin $F^{s}_{p,q}(\\mathbb{R}^n)$ of order $s$ and $0<p\\leq\\infty$, $0<q\\leq\\infty$. The results that are obtained are all up to the end-point and sharp and are also applied to the regularity of Klein-Gordon-type oscillatory integrals in the aforementioned function spaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-02-01T08:41:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35S30",
      "42B35",
      "42B37",
      "42B20"
    ],
    "keywords": [
      "fourier integral operators",
      "classical function spaces",
      "non-degenerate phase functions",
      "klein-gordon-type oscillatory integrals",
      "global boundedness"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}