{
  "id": "1311.3725",
  "version": "v2",
  "published": "2013-11-15T04:29:03.000Z",
  "updated": "2016-02-18T01:58:27.000Z",
  "title": "Sharp estimates for trilinear oscillatory integrals and an algorithm of two-dimensional resolution of singularities",
  "authors": [
    "Lechao Xiao"
  ],
  "comment": "46 pages, 8 figures; Referees' comments incorporated; to appear in Revista Matem\\'atica Iberoamericana",
  "categories": [
    "math.CA"
  ],
  "abstract": "We obtain sharp estimates for certain trilinear oscillatory integrals. In particular, we extend Phong and Stein's seminal result to a trilinear setting. This result partially answers a question raised by Christ, Li, Tao and Thiele concerning the sharp estimates for certain multilinear oscillatory integrals. The method in this paper relies on a self-contained algorithm of resolution of singularities in $\\mathbb R^2$, which may be of independent interest.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-11-15T04:29:03.000Z",
      "comment": "40 pages, 8 figures",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2016-02-18T01:58:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B20",
      "14E15"
    ],
    "keywords": [
      "trilinear oscillatory integrals",
      "sharp estimates",
      "two-dimensional resolution",
      "singularities",
      "multilinear oscillatory integrals"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 46,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1311.3725X"
    }
  }
}