{
  "abstract": "We study the Banach space and operator factorization structure of Janson-Sobolev and Janson-Sobolev-Hardy spaces. This new class of martingale spaces is determined by a $q$-adic filtration, a subspace $V\\subset \\mathbb{R}_0^{l\\times q}$, and a rearrangement invariant function space $X$. Our main result shows that, for every bounded diagonal operator $D$, the operator $S = \\sum_{t=1}^s λ_{\\mathcal U}^{k_t}(D)Q_{\\mathcal K_t}^{\\mathcal B}$ determined by the linear functionals $λ_{\\mathcal U}^{k_t}(D)$ and the canonical projections $Q_{\\mathcal K_t}^{\\mathcal B}$, almost projectionally factors through $D$ with constant $1^+$. As consequences, we obtain factorization results for diagonal operators both under a natural boundedness condition on the canonical projections and for all spaces equipped with the $L^1$-norm.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.01628",
  "author_total": 2,
  "authors": [
    {
      "name": "Krystian Kazaniecki"
    },
    {
      "name": "Richard Lechner"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bc781ysy7zbgb.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.01628",
  "fulltext_url": null,
  "id": "bc781ysy7zbgb",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.01628",
  "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.FA"
    ],
    [
      "openalex",
      "2610|Advanced Banach Space Theory"
    ]
  ],
  "openalex": "W7216224889",
  "pdf_url": "https://arxiv.org/pdf/2610.01628",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bc781ysy7zbgb.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:07Z",
      "native_id": "2610.01628",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.01628"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Diagonal operators on Janson-Sobolev and Janson-Sobolev-Hardy spaces",
  "title_text": "Diagonal operators on Janson-Sobolev and Janson-Sobolev-Hardy spaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:07Z",
  "url": "https://research.draconitic.com/paper/bc781ysy7zbgb",
  "venue": "arXiv",
  "versions": []
}