{
  "abstract": "For any convex set $Ω\\subset\\mathbb{R}^n$ that does not contain affine lines, we prove the inequality $$\\int_Ω\\frac{|\\hat{f}(x)|^2}{ω_Ω(x)}\\,dx\\leq C(n)\\|f\\|_{L^1}^2,\\quad \\supp\\hat{f}\\subsetΩ,$$ where $ω_Ω(x)=m(Ω\\cap(2x-Ω))$. As a consequence, we derive a weak factorization for $$\\PW^1(Ω)=\\{f\\in L^1(\\mathbb{R}^n):\\supp\\hat{f}\\subsetΩ\\}.$$ Furthermore, we establish a complete characterization of Schatten class Hankel operators for polyhedra for all $1\\leq p<\\infty,$ extending the already known $1\\leq p\\leq 2$ range.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.10730",
  "author_total": 1,
  "authors": [
    {
      "name": "Konstantinos Bampouras"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1gtyax2gjsht1.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.10730",
  "fulltext_url": null,
  "id": "1gtyax2gjsht1",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.10730",
  "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.FA"
    ],
    [
      "openalex",
      "2604|Advanced Harmonic Analysis Research"
    ]
  ],
  "openalex": "W7212316499",
  "pdf_url": "https://arxiv.org/pdf/2609.10730",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1gtyax2gjsht1.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:30Z",
      "native_id": "2609.10730",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.10730"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Helson Inequality, Hankel Operators, and Weak Factorization on Paley-Wiener spaces of Convex Domains",
  "title_text": "Helson Inequality, Hankel Operators, and Weak Factorization on Paley-Wiener spaces of Convex Domains",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:30Z",
  "url": "https://research.draconitic.com/paper/1gtyax2gjsht1",
  "venue": "arXiv",
  "versions": []
}