{
  "abstract": "It is well known that $u_0 \\in L^2(\\mathbb{R}) \\setminus \\{0\\}$ is an extremizer for the $L^8_t L^4_x$-Strichartz estimate if and only if it is a Gaussian. We show that every extremizing sequence of even functions $\\{ u_n \\} \\subset L^2(\\mathbb{R}) \\setminus \\{0\\}$ approaches a centered Gaussian in an appropriate sense. This result follows from a certain inequality for coordinate-wise even $L^2$ functions on $\\mathbb{R}^4$ conjectured by Gonçalves (2019) which we prove in this paper with the optimal constant.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.31543",
  "author_total": 1,
  "authors": [
    {
      "name": "Soichiro Suzuki"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9s2ae7g6qyxx9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.31543",
  "fulltext_url": null,
  "id": "9s2ae7g6qyxx9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.31543",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "arxiv",
      "math.CA"
    ],
    [
      "openalex",
      "2610|Advanced Mathematical Physics Problems"
    ]
  ],
  "openalex": "W7223347718",
  "pdf_url": "https://arxiv.org/pdf/2610.31543",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9s2ae7g6qyxx9.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:38Z",
      "native_id": "2610.31543",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.31543"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "A sharpened $L^8_t L^4_x$-Strichartz estimate for even initial data",
  "title_text": "A sharpened L^8_t L^4_x-Strichartz estimate for even initial data",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:38Z",
  "url": "https://research.draconitic.com/paper/9s2ae7g6qyxx9",
  "venue": "arXiv",
  "versions": []
}