{
  "abstract": "We prove the $L^p(\\mathbb R^n\\times\\mathbb R^m)$ boundedness of the rough product singular integral $T_Ω$, its maximal truncation $T_Ω^*$, and the product Marcinkiewicz integral $μ_Ω$ for $1<p<\\infty$, assuming that $Ω\\in H^1(S^{n-1}\\times S^{m-1})$ satisfies separate cancellation. These results include kernels in $H^1(S^{n-1}\\times S^{m-1})$ that lie outside the Orlicz classes required in earlier work. We also obtain equivalent characterizations of the product Hardy space in terms of restricted, conjugate, and spectral Riesz transforms, together with radial maximal functions, non-tangential maximal functions, and area integrals associated with the spectral and ball Poisson extensions. The operator bounds are proved using restricted Riesz transforms and the Calderón--Zygmund rotation method. For the Marcinkiewicz integral, we further establish integrable bounds for the radial profiles of the transformed kernels.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.33696",
  "author_total": 4,
  "authors": [
    {
      "name": "Jiecheng Chen"
    },
    {
      "name": "Dashan Fan"
    },
    {
      "name": "Weitao Hu"
    },
    {
      "name": "Meng Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8zw41r4gavn5x.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.33696",
  "fulltext_url": null,
  "id": "8zw41r4gavn5x",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.33696",
  "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": "W7214724463",
  "pdf_url": "https://arxiv.org/pdf/2609.33696",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8zw41r4gavn5x.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2609.33696",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.33696"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Rough Singular Integrals and Marcinkiewicz Integrals on Product Spaces, with $H^1$ Characterizations on Product Spheres",
  "title_text": "Rough Singular Integrals and Marcinkiewicz Integrals on Product Spaces, with H^1 Characterizations on Product Spheres",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/8zw41r4gavn5x",
  "venue": "arXiv",
  "versions": []
}