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On a product operator from weighted Bergman-Nevanlinna spaces to weighted Zygmund spaces. (English) Zbl 1370.47038

Summary: Let \({\mathbb D} = \{z\in {\mathbb C}: | z| <1\}\) be the open unit disk, \(\varphi\) an analytic self-map of \(\mathbb D\) and \(\psi\) an analytic function in \(\mathbb D\). Let \(\mathcal D\) be the differentiation operator and \(W_{\varphi, \psi}\) the weighted composition operator. The boundedness and compactness of the product operator \(\mathcal D W_{\varphi, \psi}\) from weighted Bergman-Nevanlinna spaces to weighted Zygmund spaces on \(\mathbb D\) are characterized.

MSC:

47B38 Linear operators on function spaces (general)
46E10 Topological linear spaces of continuous, differentiable or analytic functions
30H20 Bergman spaces and Fock spaces
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