{
  "abstract": "We prove decay estimates for oscillatory integral operators along $(y_1, y_2, y_1^2+y_2^2)$ in the finite field and the continuous settings. In the continuous setting, our result allows a bi-parameter maximal modulation, which extends the one-parameter version previously established by Pierce and Yung. Our approach is different from theirs. Then we discuss three applications of our estimates: a power saving bound for certain pattern finding problem in finite fields, a short approach to $L^p$ boundedness of an one-parameter Pierce--Yung operator, and $L^p$ boundedness of a bi-parameter Pierce--Yung operator.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.14841",
  "author_total": 1,
  "authors": [
    {
      "name": "Jianghao Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/d8xnymh85fg7w.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.14841",
  "fulltext_url": null,
  "id": "d8xnymh85fg7w",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.14841",
  "language": null,
  "licence": "CC-BY-SA-4.0",
  "licence_label": "CC BY-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CA"
    ],
    [
      "openalex",
      "2604|Advanced Harmonic Analysis Research"
    ]
  ],
  "openalex": "W7221833881",
  "pdf_url": "https://arxiv.org/pdf/2610.14841",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/d8xnymh85fg7w.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.14841",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.14841"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Oscillatory Integral Operators Along the Paraboloid and Applications",
  "title_text": "Oscillatory Integral Operators Along the Paraboloid and Applications",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/d8xnymh85fg7w",
  "venue": "arXiv",
  "versions": []
}