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Extended Cesáro operators between different weighted Bloch-type spaces. (Chinese. English summary) Zbl 1174.30335

Summary: In this paper the extended Cesáro operator \(T_g\) is characterized between the \(\alpha\)-Bloch spaces \(\beta_\alpha\) and the logarithmic weighted Bloch space \(\beta_L\) on the unit disc. Some necessary and sufficient conditions are given for \(T_g\) to be a bounded operator or a compact operator from \(\beta_L(\beta_\alpha)\) to \(\beta_\alpha(\beta_L).\)

MSC:

30D05 Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable
30H05 Spaces of bounded analytic functions of one complex variable
47B38 Linear operators on function spaces (general)
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