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Generalized integration operators between Bloch-type spaces and \(F(p,q,s)\) spaces - MaRDI portal

Generalized integration operators between Bloch-type spaces and \(F(p,q,s)\) spaces (Q373705)

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scientific article; zbMATH DE number 6219271
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Generalized integration operators between Bloch-type spaces and \(F(p,q,s)\) spaces
scientific article; zbMATH DE number 6219271

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    Generalized integration operators between Bloch-type spaces and \(F(p,q,s)\) spaces (English)
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    24 October 2013
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    generalized integration operator
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    Bloch-type space
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    \(F(p,q,s)\)-space
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    Let \(H({\mathbb D})\) be the space of all holomorphic functions on the unit disk \(\mathbb D\) in the complex plane. Let \(\varphi\in H({\mathbb D})\), \(\varphi:{\mathbb D}\to {\mathbb D}\), \(n\) be a positive integer, \(g\in H({\mathbb D})\). The authors investigate operators of the form NEWLINE\[NEWLINE (I_{g,\varphi}^{(n)}f)(z) = \int_{0}^{z}f^{(n)}(\varphi(\zeta))g(\zeta)\,d\zeta,\quad z\in {\mathbb D}, NEWLINE\]NEWLINE between Bloch-type spaces and \(F(p,q,s)\)-spaces. They obtain necessary and sufficient conditions for boundedness and compactness of these operators and two-sided norm estimates in the case of boundedness.
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