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Volterra Type Operators Between Bloch Type Spaces and Weighted Banach Spaces

  • Qingze LinEmail author
Article
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Abstract

When the weight \(\mu \) is more general than normal, the complete characterizations in terms of the symbol g and weights for the conditions of the boundedness and compactness of \(T_g: H^{\infty }_\nu \rightarrow H^{\infty }_\mu \) and \(S_g: H^{\infty }_\nu \rightarrow H^{\infty }_\mu \) are still unknown. Smith et al. firstly gave the sufficient and necessary conditions for the boundedness of Volterra type operators on Banach spaces of bounded analytic functions when the symbol functions are univalent. In this paper, continuing their lines of investigations, we give the complete characterizations of the conditions for the boundedness and compactness of Volterra type operators \(T_g\) and \(S_g\) between Bloch type spaces \({\mathcal {B}}^\infty _\nu \) and weighted Banach spaces \(H^{\infty }_\nu \) with more general weights, which generalize their works.

Keywords

Volterra type operator Boundedness Compactness Weighted Banach space Bloch type space 

Mathematics Subject Classification

Primary 47G10 Secondary 30H05 

Notes

Acknowledgements

It is a pleasure to express our gratitude to the referee for his(or her) valuable comments and helpful suggestions which have greatly improved the appearance of this paper.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.School of Applied MathematicsGuangdong University of TechnologyGuangzhouPeople’s Republic of China

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