Characterizations of boundedness, compactness, and Hilbert-Schmidt property for composition-differentiation operators on weighted Dirichlet spaces are given, with essential norm estimates via the generalized Nevanlinna counting function.
Zhu, Operator theory in function spaces, Math
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Composition-differentiation operators on weighted Dirichlet spaces
Characterizations of boundedness, compactness, and Hilbert-Schmidt property for composition-differentiation operators on weighted Dirichlet spaces are given, with essential norm estimates via the generalized Nevanlinna counting function.