{
  "id": "1710.10349",
  "version": "v1",
  "published": "2017-10-27T22:08:28.000Z",
  "updated": "2017-10-27T22:08:28.000Z",
  "title": "Sharp estimates for oscillatory integral operators via polynomial partitioning",
  "authors": [
    "Larry Guth",
    "Jonathan Hickman",
    "Marina Iliopoulou"
  ],
  "comment": "83 pages. 4 figures",
  "categories": [
    "math.CA"
  ],
  "abstract": "The sharp range of $L^p$-estimates for the class of H\\\"ormander-type oscillatory integral operators is established in all dimensions under a positive-definite assumption on the phase. This is achieved by generalising a recent approach of the first author for studying the Fourier extension operator, which utilises polynomial partitioning arguments.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-10-27T22:08:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B20"
    ],
    "keywords": [
      "oscillatory integral operators",
      "sharp estimates",
      "fourier extension operator",
      "utilises polynomial partitioning arguments",
      "positive-definite assumption"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 83,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}