{
  "abstract": "Let $T$ be a convolution Calderón--Zygmund operator satisfying Hytönen's non-degeneracy condition. We prove that, for every $p\\in(1,\\infty)$ and $m\\ge3$, there exists a positive constant $C$ such that, for any $t\\in[1,\\infty)$, \\begin{equation*} \\sup_{[W]_{\\mathcal A_p}\\le t} \\|T\\|_{L^p(W)\\to L^p(W)} \\ge C t^{1+\\frac{1}{p(p-1)}}, \\end{equation*} where the supremum is taken over all matrix weights $W:\\ \\mathbb R^n\\to\\mathbb C^{m\\times m}$ with their weight constants $[W]_{\\mathcal A_p}\\le t$. If, in addition, the odd part of the kernel is non-degenerate (such as the Hilbert transform and the Riesz transforms), the same conclusion holds for every $m\\ge2$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.33560",
  "author_total": 3,
  "authors": [
    {
      "name": "Fan Bu"
    },
    {
      "name": "Dachun Yang"
    },
    {
      "name": "Wen Yuan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7hp7xy9vfjz34.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.33560",
  "fulltext_url": null,
  "id": "7hp7xy9vfjz34",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.33560",
  "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",
      "2604|Advanced Harmonic Analysis Research"
    ]
  ],
  "openalex": "W7214736485",
  "pdf_url": "https://arxiv.org/pdf/2609.33560",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7hp7xy9vfjz34.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2609.33560",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.33560"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Sharp Matrix-Weighted Lower Bounds for Non-Degenerate Convolution Calderón--Zygmund Operators",
  "title_text": "Sharp Matrix-Weighted Lower Bounds for Non-Degenerate Convolution Calderón--Zygmund Operators",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/7hp7xy9vfjz34",
  "venue": "arXiv",
  "versions": []
}