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Bloch type spaces of analytic functions. (English) Zbl 0787.30019

Summary: For \(\alpha>0\) let \({\mathcal B}_ \alpha\) denote the space of analytic functions \(f\) on the unit disk \(\mathbb{D}\) satisfying \[ \sup\bigl\{(1-| z|^ 2)^ \alpha| f'(z)|: z\in \mathbb{D}\bigr\}< +\infty. \] The paper studies various properties of the spaces \({\mathcal B}_ \alpha\), including duality, Lipschitz space structure, pointwise multipliers, and coefficient multipliers. The paper also contains several results about the boundary behavior and coefficient growth for functions in \({\mathcal B}_ \alpha\).

MSC:

30D45 Normal functions of one complex variable, normal families
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References:

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