{
  "abstract": "The commutators of intrinsic square functions associated with the intrinsic Littlewood--Paley $g$-function, the intrinsic $g_λ^{*}$-function and the intrinsic Lusin area function can be used to characterize BMO-type function spaces through their boundedness properties. In this paper, we show that, for $b\\in {\\rm BMO}(\\mathbb{R}^{n})$, the boundedness of each of these commutators from the Musielak--Orlicz Hardy space $H^φ(\\mathbb{R}^{n})$ to $L^φ(\\mathbb{R}^{n})$ is equivalent to $b\\in {\\rm BMO}_φ(\\mathbb{R}^{n})$ (a nontrivial subspace of $\\rm{BMO}(\\mathbb{R}^{n})$), under suitable assumptions on the growth function $φ$. This extends the weighted characterization of Han and Wu [Proc. Amer. Math. Soc. 152(1) (2024), 281--293] to the Musielak--Orlicz setting. In addition, under suitable assumptions on a growth function $Φ$, we prove that, for $b\\in {\\rm BMO}_Φ(\\mathbb{R}^{n})$, these commutators are bounded from the $b$-adapted Orlicz--Hardy space $H_{b}^Φ(\\mathbb{R}^{n})$ to $L^{1}(\\mathbb{R}^{n})$ and from Orlicz Hardy space $H^Φ(\\mathbb{R}^{n})$ to $L^{1,\\infty}(\\mathbb{R}^{n})$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.15610",
  "author_total": 4,
  "authors": [
    {
      "name": "Yanyan Han"
    },
    {
      "name": "Feng Liu"
    },
    {
      "name": "Yongming Wen"
    },
    {
      "name": "Huoxiong Wu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7tqqvvxfdyqc1.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.15610",
  "fulltext_url": null,
  "id": "7tqqvvxfdyqc1",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.15610",
  "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": "W7213367845",
  "pdf_url": "https://arxiv.org/pdf/2609.15610",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7tqqvvxfdyqc1.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:29Z",
      "native_id": "2609.15610",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.15610"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "BMO-Type characterizations and endpoint estimates for commutators of intrinsic square functions on Orlicz-Hardy spaces",
  "title_text": "BMO-Type characterizations and endpoint estimates for commutators of intrinsic square functions on Orlicz-Hardy spaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/7tqqvvxfdyqc1",
  "venue": "arXiv",
  "versions": []
}