Weighted differentiation composition operators from H^∞ to Zygmund spaces

Abstract

Let ϕ be an analytic self-map of the unit disk 𝔻, H(𝔻) the space of analytic functions on 𝔻 and u∈H(𝔻). The boundedness and compactness of the weighted differentiation composition operator , where n∈ℕ₀, from H ^∞ to Zygmund space are investigated in this paper.

Keywords:

• boundedness
• compactness
• weighted differentiation composition operators
• bounded analytic function
• Zygmund space

AMS Subject Classifications :

• 47B38
• 47B33
• 30H05
• 30D45
• 46E15

Acknowledgements

The second author thanks Professors Shaozong Yan and Xiaoman Chen for their encouragement and help while visiting Fudan University. The authors acknowledge gratefully the support in part by the National Natural Science Foundation of China (No. 10471039) and the Grant of Higher Schools’ Natural Science Basic Research of Jiangsu Province of China (Nos. 06KJD110175; 07KJB110115). The authors also thank the referees for their thoughtful comments and helpful suggestions and for bringing important references to our attention.