Composition-differentiation operators on weighted Dirichlet spaces
Anirban Sen, Somdatta Barik, Kallol paul
TL;DR
This paper characterizes various boundedness properties of composition-differentiation operators on weighted Dirichlet spaces, providing norm estimates and examples to illustrate their behavior.
Contribution
It offers a comprehensive characterization of bounded, compact, and Hilbert-Schmidt composition-differentiation operators on weighted Dirichlet spaces, including essential norm estimates.
Findings
Characterization of bounded, compact, and Hilbert-Schmidt operators
Estimation of essential norm via asymptotic behavior of a function
Norm estimates for specific inducing maps and illustrative examples
Abstract
We characterize bounded, compact, and Hilbert-Schmidt composition-differentiation operators on weighted Dirichlet spaces. The essential norm is estimated via the asymptotic behavior of a function that involves the generalized Nevanlinna counting function of the inducing map. Norm estimates for particular inducing maps are given, and examples are provided to demonstrate the applicability of the results.
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