{
  "abstract": "Let $f$ be a nonzero holomorphic germ at $0 \\in \\mathbb C^n$ with $f(0)=0$, and let $χ$ be a $C^2$ non-decreasing convex function on the left half-line. We establish sharp necessary and sufficient conditions for the local Sobolev regularity of the plurisubharmonic function $v=χ(\\log|f|).$ The criteria for the $L^p$-integrability of the classical Laplacian and for $W^{1,p}$-regularity are given by a weighted integral involving $χ''$ and $χ'$, respectively, and depend on $f$ only through the smallest multiplicity of $\\operatorname{Div}(f)$. We also obtain the $W^{2,p}_{\\mathrm{loc}}$ criterion for $1<p<\\infty$. At the endpoint $p=1$, we prove that \\[ v\\in W^{2,1}_{\\mathrm{loc}} \\quad\\Longleftrightarrow\\quad χ'\\in L^1((-\\infty,A)), \\] equivalently, $v$ is locally bounded. As applications, we obtain counterexamples to Calderón-Zygmund theory and characterize a class of functions in the local Monge--Ampère domain. % and exhibit a natural family in $W^{2,1}_{\\mathrm{loc}}$ whose limit fails to belong to $W^{2,1}_{\\mathrm{loc}}$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.39136",
  "author_total": 3,
  "authors": [
    {
      "name": "Hongrong Chen"
    },
    {
      "name": "Guokuan Shao"
    },
    {
      "name": "Wenxuan Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dtaz095597hc8.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.39136",
  "fulltext_url": null,
  "id": "dtaz095597hc8",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.39136",
  "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.CV"
    ],
    [
      "openalex",
      "2608|Analytic and geometric function theory"
    ]
  ],
  "openalex": "W7215097348",
  "pdf_url": "https://arxiv.org/pdf/2609.39136",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dtaz095597hc8.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:49Z",
      "native_id": "2609.39136",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.39136"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Characterization of Sobolev regularity of plurisubharmonic functions",
  "title_text": "Characterization of Sobolev regularity of plurisubharmonic functions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:49Z",
  "url": "https://research.draconitic.com/paper/dtaz095597hc8",
  "venue": "arXiv",
  "versions": []
}