{
  "abstract": "We study $L^p$--$L^q$ boundedness of the strong circular maximal operator $\\M$, the maximal function over axis-parallel ellipses centered at the origin whose two semiaxes range independently over $[1,2]$. We prove that $\\M$ is bounded from $L^p$ to $L^q$ whenever $(1/p,1/q)$ lies in the interior of the triangle with vertices $(0,0)$, $(2/7,1/7)$, and $(1/3,1/3)$, the two-parameter analogue of the triangle with vertices $(0,0)$, $(2/5,1/5)$, and $(1/2,1/2)$ obtained by Schlag and Schlag--Sogge for the circular maximal function. The range is sharp up to the boundary; in particular, weak type $(p,q)$ bounds fail for every $p\\le3$. The proof is based on a bilinear estimate for frequencies in separated angular sectors, uniform as the sectors approach the coordinate axes. We also prove the analogous sharp result for axis dilations of a translated circle $c+\\mathbb S^1$ with fixed $c\\ne0$, where the vertex $(2/7,1/7)$ is replaced by $(1/4,1/8)$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.34691",
  "author_total": 4,
  "authors": [
    {
      "name": "Jin Bong Lee"
    },
    {
      "name": "Sanghyuk Lee"
    },
    {
      "name": "Seunghwan Lee"
    },
    {
      "name": "Jeongtae Oh"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fvfcta7e6k47d.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.34691",
  "fulltext_url": null,
  "id": "fvfcta7e6k47d",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.34691",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CA"
    ],
    [
      "openalex",
      "2604|Advanced Harmonic Analysis Research"
    ]
  ],
  "openalex": "W7223933736",
  "pdf_url": "https://arxiv.org/pdf/2610.34691",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fvfcta7e6k47d.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2610.34691",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.34691"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Sharp $L^p$--$L^q$ bounds for the strong circular maximal operator",
  "title_text": "Sharp L^p--L^q bounds for the strong circular maximal operator",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/fvfcta7e6k47d",
  "venue": "arXiv",
  "versions": []
}