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Weighted composition operators between the little \(\alpha\)-Bloch spaces and the logarithmic Bloch space. (Weighted composition operator between the little \(\alpha\)-Bloch spaces and the logarithmic Bloch.) (English) Zbl 1152.47019

In this interesting paper, the author characterizes the boundedness and compactness of the weighted composition operator \(uC_\varphi\) between the logarithmic Bloch space \(\beta_L\) and the little \(\alpha\)-Bloch spaces \(\beta^0_\alpha\) on the unit disk. Some necessary and sufficient conditions are given for which \(uC_\varphi\) is a bounded or compact operator between \(\beta_L\) and \(\beta^0_\alpha\).

MSC:

47B33 Linear composition operators
30H05 Spaces of bounded analytic functions of one complex variable
30D05 Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable
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