{
  "abstract": "We prove that, on a non-compact Ahlfors-regular PI space, every function of bounded variation $f$ can be decomposed as a countable sum $\\sum_{n=1}^\\infty f_n$ of monotone functions of bounded variation $f_n$, in such a way that the total variation of $f$ is the sum of the total variations of the functions $f_n$. Our result extends a Euclidean result of Bianchini and Tonon to the metric setting.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.14779",
  "author_total": 3,
  "authors": [
    {
      "name": "Paolo Bonicatto"
    },
    {
      "name": "Panu Lahti"
    },
    {
      "name": "Enrico Pasqualetto"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7b5wp92yzdkqv.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.14779",
  "fulltext_url": null,
  "id": "7b5wp92yzdkqv",
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  "landing_url": "https://arxiv.org/abs/2610.14779",
  "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",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7221828926",
  "pdf_url": "https://arxiv.org/pdf/2610.14779",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7b5wp92yzdkqv.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.14779",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.14779"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Decomposition of functions of bounded variation in Ahlfors-regular PI spaces",
  "title_text": "Decomposition of functions of bounded variation in Ahlfors-regular PI spaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/7b5wp92yzdkqv",
  "venue": "arXiv",
  "versions": []
}