{
  "id": "1905.07980",
  "version": "v1",
  "published": "2019-05-20T10:37:14.000Z",
  "updated": "2019-05-20T10:37:14.000Z",
  "title": "Sharp Bounds for Oscillatory Integral Operators with Homogeneous Polynomial Phases",
  "authors": [
    "Danqing He",
    "Zuoshunhua Shi"
  ],
  "comment": "14 pages",
  "categories": [
    "math.CA"
  ],
  "abstract": "We obtain sharp $L^p$ bounds for oscillatory integral operators with generic homogeneous polynomial phases in several variables. The phases considered in this paper satisfy the rank one condition which is an important notion introduced by Greenleaf, Pramanik and Tang. Under certain additional assumptions, we can establish sharp damping estimates with critical exponents to prove endpoint $L^p$ estimates.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-05-20T10:37:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B20",
      "47G10"
    ],
    "keywords": [
      "oscillatory integral operators",
      "sharp bounds",
      "generic homogeneous polynomial phases",
      "paper satisfy",
      "establish sharp damping estimates"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}