{
  "abstract": "We prove Mizohata--Takeuchi-type estimates for the Fourier extension operator associated with the truncated hyperbolic paraboloid in $\\R^3$. Our main result controls the weighted $L^2$ norm of the extension operator by the $L^2$ mass of the weight over a multiscale family of parallelepipeds arising from $\\ell^2$ decoupling for the hyperbolic paraboloid. We deduce this result from a weighted $L^2$ estimate for functions whose Fourier transforms are supported in a small neighborhood of the hyperbolic paraboloid, which we establish using a bilinear refined decoupling estimate.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.07909",
  "author_total": 2,
  "authors": [
    {
      "name": "Jongchon Kim"
    },
    {
      "name": "Liang Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dy7zqd3eczyv8.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.07909",
  "fulltext_url": null,
  "id": "dy7zqd3eczyv8",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.07909",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CA"
    ],
    [
      "openalex",
      "2604|Advanced Harmonic Analysis Research"
    ]
  ],
  "openalex": "W7220971735",
  "pdf_url": "https://arxiv.org/pdf/2610.07909",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dy7zqd3eczyv8.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:37Z",
      "native_id": "2610.07909",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.07909"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "A Mizohata--Takeuchi-type estimate for the hyperbolic paraboloid",
  "title_text": "A Mizohata--Takeuchi-type estimate for the hyperbolic paraboloid",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:31Z",
  "url": "https://research.draconitic.com/paper/dy7zqd3eczyv8",
  "venue": "arXiv",
  "versions": []
}