Integral-type operators from weighted Bloch spaces into Bergman-type spaces

Abstract

Let ϕ be an analytic self-map and u be a fixed analytic function on the open unit disk 𝔻 in the complex plane ℂ. The following integral-type operators

have recently attracted a lot of attention. In this article, we characterize the boundedness and compactness of operators I _g and J _g from weighted Bloch spaces into Bergman-type spaces.

Keywords:

• Bergman-type spaces
• logarithmic Bloch spaces
• integral-type operators

2000 AMS Subject Classification :

• 47B38
• 47B33
• 30D55
• 46E15

Acknowledgements

The second author thanks Professors Shaozong Yan and Xiaoman Chen for their encouragement and help while visiting Fudan University. The authors also wish to thank the referee(s) for carefully reading the manuscript and making several useful suggestions that greatly improved the final version of this paper. Supported by the Natural Science Foundation of China (10471039) and the grant of higher schools’ natural science basic research of Jiangsu Province of China (06KJD110175, 07KJB110115).