{
  "id": "1901.01487",
  "version": "v1",
  "published": "2019-01-06T02:15:05.000Z",
  "updated": "2019-01-06T02:15:05.000Z",
  "title": "Improved variable coefficient square functions and local smoothing of Fourier integral operators",
  "authors": [
    "Chuanwei Gao",
    "Changxing Miao",
    "Jianwei-Urbain Yang"
  ],
  "comment": "30pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We establish certain square function estimates for a class of oscillatory integral operators with homogeneous phase functions. These results are employed to deduce a refinement of a previous result of Mockenhaupt Seeger and Sogge \\cite{MSS-jams} on the local smoothing property for Fourier integral operators, which arise naturally in the study of wave equations on compact Riemannian manifolds. The proof is an adaptation of the bilinear approach of Tao and Vargas \\cite{Tao-Vargas-II}, %as well as Garrig\\'os and Seeger \\cite{GaSe09}, and based on bilinear oscillatory integral estimates of Lee \\cite{Lee-JFA}.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-01-06T02:15:05.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "fourier integral operators",
      "variable coefficient square functions",
      "local smoothing",
      "bilinear oscillatory integral estimates",
      "compact riemannian manifolds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}