{
  "id": "1804.03605",
  "version": "v2",
  "published": "2018-04-10T15:57:10.000Z",
  "updated": "2019-11-08T15:52:50.000Z",
  "title": "Extremizability of Fourier restriction to the paraboloid",
  "authors": [
    "Betsy Stovall"
  ],
  "comment": "Some typos were corrected and arguments expanded in several places",
  "doi": "10.1016/j.aim.2019.106898",
  "categories": [
    "math.CA"
  ],
  "abstract": "In this article, we prove that all global, nonendpoint Fourier restriction inequalities for the paraboloid in $\\mathbb R^{1+d}$ have extremizers and that $L^p$-normalized extremizing sequences are precompact modulo symmetries. This result had previously been established for the case $q=2$. In the range where the boundedness of the restriction operator is still an open question, our result is conditional on improvements toward the restriction conjecture.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2019-11-08T15:52:50.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "paraboloid",
      "extremizability",
      "nonendpoint fourier restriction inequalities",
      "precompact modulo symmetries",
      "restriction conjecture"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Elsevier"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}