Composition-differentiation operators on weighted Dirichlet spaces
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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