{
  "abstract": "We study the membership of commutators $[b,T]$ of Calderón--Zygmund operators in the Schatten--Lorentz classes in the matrix-weighted setting. Working on a space of homogeneous type $(X,ρ,μ)$ with a matrix $A_2$ weight $W$, we characterise, for $p\\in(1,\\infty)$ and $q\\in[1,\\infty)$, the Schatten--Lorentz norm $\\|[b,T]\\|_{S^{p,q}(L^2(W))}$ in terms of an oscillation (Besov-type) norm $\\|b\\|_{\\mathrm{Osc}^{p,q}}$ of the symbol: for all $p\\in(1,\\infty)$, finiteness of $\\|b\\|_{\\mathrm{Osc}^{p,q}}$ is necessary; and for $p>p(η)$, where $p(η)$ depends on the regularity of the kernel of $T$ and a dimensional parameter of the space, the two-sided estimate $\\|[b,T]\\|_{S^{p,q}(L^2(W))}\\approx\\|b\\|_{\\mathrm{Osc}^{p,q}}$ holds. Extending a recent unified framework for unweighted and scalar-weighted versions of such results by one of us to the matrix-weighted setting, our approach combines the dyadic representation of singular integral operators with the nearly weakly orthogonal (NWO) sequences of Rochberg and Semmes.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.16476",
  "author_total": 2,
  "authors": [
    {
      "name": "Tuomas Hytönen"
    },
    {
      "name": "Xingyan Quan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1qf8q3wq6pcw5.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.16476",
  "fulltext_url": null,
  "id": "1qf8q3wq6pcw5",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.16476",
  "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": "W7221800520",
  "pdf_url": "https://arxiv.org/pdf/2610.16476",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1qf8q3wq6pcw5.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.16476",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.16476"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Schatten--Lorentz properties of commutators with matrix weights",
  "title_text": "Schatten--Lorentz properties of commutators with matrix weights",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/1qf8q3wq6pcw5",
  "venue": "arXiv",
  "versions": []
}