{
  "id": "2308.05631",
  "version": "v1",
  "published": "2023-08-10T15:19:07.000Z",
  "updated": "2023-08-10T15:19:07.000Z",
  "title": "Some new decay estimates for $(2+1)$-dimensional degenerate oscillatory integral operators",
  "authors": [
    "Yuxin Tan",
    "Shaozhen Xu"
  ],
  "categories": [
    "math.CA"
  ],
  "abstract": "In this paper, we consider the $(2+1)-$dimensional oscillatory integral operators with cubic homogeneous polynomial phases, which are degenerate in the sense of \\cite{Tan06}. We improve the previously known $L^2\\to L^2$ decay rate to $3/8$ and also establish a sharp $L^2\\to L^6$ decay estimate based on fractional integration method.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-08-10T15:19:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B20",
      "47G10"
    ],
    "keywords": [
      "dimensional degenerate oscillatory integral operators",
      "decay estimate",
      "dimensional oscillatory integral operators",
      "cubic homogeneous polynomial phases",
      "fractional integration method"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}