{
  "abstract": "In this paper, we prove boundedness on $L^p(\\mathbb{R}^{n+1})$, $1<p<\\infty$, of polynomial Carleson operators along the paraboloid with phase belonging to a class $Y$ of homogeneous polynomials. For $n,d\\ge 2$, let $\\mathcal{P}^{n,d}$ denote the class of all real-valued homogeneous polynomials in $n$ variables of degree $d$. We may take the class $Y$ to be an arbitrary linear subspace $Y \\subseteq \\mathcal{P}^{n,d}$ such that $\\dim Y \\le M_{n , d}$, where $M_{n , d}$ is a constant depending only on $n$ and $d$. The main novelty of our result is that we may allow a large collection of homogeneous polynomials of the same degree, in contrast to earlier results that relied on distinct degree assumptions. The heart of our proof is a $TT^*$ method, and the derivation of new estimates for oscillatory integral kernels involving interactions between homogeneous polynomial phases and the paraboloid.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.05931",
  "author_total": 1,
  "authors": [
    {
      "name": "Alina Zhu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2nx9w9c8s61jk.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.05931",
  "fulltext_url": null,
  "id": "2nx9w9c8s61jk",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.05931",
  "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.CA"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.05931",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2nx9w9c8s61jk.ris",
  "sources": [
    {
      "first_seen": "2026-11-05T15:21:00Z",
      "native_id": "2611.05931",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.05931"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Homogeneous Polynomial Carleson Operators Along the Paraboloid",
  "title_text": "Homogeneous Polynomial Carleson Operators Along the Paraboloid",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:30Z",
  "url": "https://research.draconitic.com/paper/2nx9w9c8s61jk",
  "venue": "arXiv",
  "versions": []
}