{
  "abstract": "We study weighted composition-differentiation operators of order $n,$ $D^n_{ψ,φ}f:= ψ\\cdot f^{(n)}\\circ φ$ on weighted Dirichlet spaces. Our main goal is to describe the operator-theoretic properties of $D^n_{ψ,φ}$ in terms of the inducing functions $ψ$ and $φ.$ We characterize bounded, compact, and Hilbert-Schmidt class of such operators and estimate their essential norms. Our approach relies on Carleson measures and the asymptotic behavior of inducing functions. Furthermore, we prove that $D^n_{ψ,φ}$ is bounded for all $ψ$ in the space precisely when $\\|φ\\|_\\infty<1$ and $φ$ belongs to the multiplier algebra of the space. Finally, we give norm estimates for particular elliptic inducing functions and provide examples to demonstrate our results.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.00213",
  "author_total": 3,
  "authors": [
    {
      "name": "Somdatta Barik"
    },
    {
      "name": "Anirban Sen"
    },
    {
      "name": "Kallol Paul"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5w010qbngdb71.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.00213",
  "fulltext_url": null,
  "id": "5w010qbngdb71",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.00213",
  "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|Holomorphic and Operator Theory"
    ]
  ],
  "openalex": "W7160089509",
  "pdf_url": "https://arxiv.org/pdf/2605.00213",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5w010qbngdb71.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:42Z",
      "native_id": "2605.00213",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.00213"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Weighted Composition-differentiation operators on weighted Dirichlet spaces",
  "title_text": "Weighted Composition-differentiation operators on weighted Dirichlet spaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:42Z",
  "url": "https://research.draconitic.com/paper/5w010qbngdb71",
  "venue": "arXiv",
  "versions": []
}