Weighted Composition-differentiation operators on weighted Dirichlet spaces

@misc{barik2026weighted,
  title = {{Weighted Composition-differentiation operators on weighted Dirichlet spaces}},
  author = {Somdatta Barik and Anirban Sen and Kallol Paul},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2605.00213},
  eprint = {2605.00213},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2605.00213},
}

TY  - UNPB
TI  - Weighted Composition-differentiation operators on weighted Dirichlet spaces
AU  - Somdatta Barik
AU  - Anirban Sen
AU  - Kallol Paul
PY  - 2026
DA  - 2026/10/07
PB  - arXiv
DO  - 10.48550/arxiv.2605.00213
UR  - https://arxiv.org/abs/2605.00213
AB  - We study weighted composition-differentiation operators of order n, D^n_ψ,φf:= ψ· f^(n)∘ 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|_∞<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.
ER  -