{
  "id": "2304.01092",
  "version": "v1",
  "published": "2023-04-03T15:52:22.000Z",
  "updated": "2023-04-03T15:52:22.000Z",
  "title": "The Proof of restriction conjecture In $\\mathbb{R}^{3}$",
  "authors": [
    "Hoyoung Song"
  ],
  "comment": "17 pages",
  "categories": [
    "math.CA"
  ],
  "abstract": "If S is a smooth compact surface in $\\mathbb{R}^{3}$ with strictly positive second fundamental form, and $E_S$ is the corresponding extension operator, then we prove that for all $p > 3$, $\\left\\|E_S f\\right\\|_{L^p\\left(\\mathbb{R}^3\\right)} \\leq C(p, S)\\|f\\|_{L^{\\infty}(S)}.$ The proof of restriction conjecture in $\\mathbb{R}^{3}$ implies that Kakeya set conjecture is true when n=3.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-04-03T15:52:22.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "restriction conjecture",
      "strictly positive second fundamental form",
      "smooth compact surface",
      "kakeya set conjecture",
      "corresponding extension operator"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}