从双曲α-Bloch 空间到双曲{\boldmath QK型空间上的复合算子

Abstract

Abstract:

Suppose φ is an analytic map of the unit disk D into itself, X is a Banach space of analytic functions on D.
Define the composition operator C_φ: C_φ(f)=f ο φ , for all f ∈ X. In this paper, the boundedness of the composition operators from hyperbolic α-Bloch spaces into hyperbolic Q_K type spaces are discussed, where 0 < α ≤ 1. Moreover, a necessary and sufficient condition for C_φ from weighted Dirichlet space D_p, αto Q_K(p, q) to be bounded or compact is given in terms of the map φ.

Key words: Composition operator, Analytic function, Weighted Dirichlet space

CLC Number:

47B38

YU Yan-Yan, LIU Yong-Min. Composition Operators from Hyperbolic α-Bloch Spaces into Hyperbolic Q_K Type Spaces[J].Acta mathematica scientia,Series A, 2009, 29(5): 1311-1320.

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Composition Operators from Hyperbolic α-Bloch Spaces into Hyperbolic Q_K Type Spaces

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Composition Operators from Hyperbolic α-Bloch Spaces into Hyperbolic QK Type Spaces

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Composition Operators from Hyperbolic α-Bloch Spaces into Hyperbolic Q_K Type Spaces