{
  "abstract": "In this paper, we establish a Fefferman--Stein inequality in terms of area function and non-tangential maximal function associated with the Schrödinger operator $\\mathcal{L} = -Δ+ V$ on stratified Lie groups $\\mathcal G$, where $Δ$ denotes the sub-Laplacian on $\\mathcal G$ and $V$ is a nonnegative locally integrable function. As an application, we extend this inequality to the tensor product $\\mathcal G_1 \\times \\mathcal G_2$ of two stratified Lie groups and develop atomic decompositions associated with the Schrödinger operator for functions in the Orlicz space $L\\log^{+}L(\\mathcal G_1 \\times \\mathcal G_2).$ Using these atomic decompositions, we further prove weak-type endpoint estimates for the area integral operator and the Riesz transforms associated with the Schrödinger operator on $L\\log^{+}L(\\mathcal G_1 \\times \\mathcal G_2),$ thereby extending the celebrated result of R.\\,Fefferman and E.M.\\,Stein \\cite{FSt1982} to the setting of singular integrals with non-smooth kernels.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.08193",
  "author_total": 4,
  "authors": [
    {
      "name": "Ji Li"
    },
    {
      "name": "Wanjun Li"
    },
    {
      "name": "Liang Song"
    },
    {
      "name": "Lixin Yan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/229cmha7x2grx.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.08193",
  "fulltext_url": null,
  "id": "229cmha7x2grx",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.08193",
  "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.AP"
    ],
    [
      "openalex",
      "2604|Advanced Harmonic Analysis Research"
    ]
  ],
  "openalex": "W7212035818",
  "pdf_url": "https://arxiv.org/pdf/2609.08193",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/229cmha7x2grx.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2609.08193",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.08193"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Fefferman--Stein type inequalities via area and maximal functions for Schrödinger operators with applications",
  "title_text": "Fefferman--Stein type inequalities via area and maximal functions for Schrödinger operators with applications",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/229cmha7x2grx",
  "venue": "arXiv",
  "versions": []
}