{
  "abstract": "We develop a finite-tree formalism for sharp inequalities on real-valued, mean-centered $\\operatorname{L}^1$-BMO over homogeneous $q$-ary filtrations. A reduction theorem identifies local and global sharp constants with the supremum of finite-depth constants. Finite anchoring gives compact optimization problems and rational extremizers under rational piecewise-linear hypotheses, while stable centering shows that imposing zero root average preserves the supremum over all depths. The principal application is the absolute-value map: we construct centered examples in which taking absolute values increases the BMO seminorm and obtain bounds strictly below the universal factor $2$. Jensen-defect Carleson functionals and martingale-difference envelopes provide further applications, illustrating distinct anchoring mechanisms and the differences between finite-depth rationality, stabilization, and global attainment.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.14459",
  "author_total": 1,
  "authors": [
    {
      "name": "Mohammadreza Mohajer"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/c66dymbntvhd2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.14459",
  "fulltext_url": null,
  "id": "c66dymbntvhd2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.14459",
  "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"
    ],
    [
      "arxiv",
      "math.FA"
    ],
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2604|Advanced Harmonic Analysis Research"
    ]
  ],
  "openalex": "W7221813522",
  "pdf_url": "https://arxiv.org/pdf/2610.14459",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/c66dymbntvhd2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.14459",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.14459"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Sharp Constants and Extremizers in Homogeneous Tree BMO",
  "title_text": "Sharp Constants and Extremizers in Homogeneous Tree BMO",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/c66dymbntvhd2",
  "venue": "arXiv",
  "versions": []
}