Complex Analysis and Operator Theory

, Volume 6, Issue 1, pp 121–137

Composition Followed by Differentiation Between H and Zygmund Spaces

Article

DOI: 10.1007/s11785-010-0080-7

Cite this article as:
Liu, Y. & Yu, Y. Complex Anal. Oper. Theory (2012) 6: 121. doi:10.1007/s11785-010-0080-7

Abstract

Let \({\varphi}\) be an analytic self-map of the unit disk \({\mathbb{D}}\), \({H(\mathbb{D})}\) the space of analytic functions on \({\mathbb{D}}\) and \({g \in H(\mathbb{D})}\). The boundedness and compactness of the operator \({DC_\varphi : H^\infty \rightarrow { \mathcal Z}}\) are investigated in this paper.

Keywords

Boundedness Compactness Composition operator Differentiation operator Zygmund space 

Mathematics Subject Classification (2000)

Primary 47B38 47B33 30H05 Secondary 30D45 46E15 

Copyright information

© Springer Basel AG 2010

Authors and Affiliations

  1. 1.Department of MathematicsXuzhou Normal UniversityXuzhouPeople’s Republic of China
  2. 2.School of Mathematics and Physics ScienceXuzhou Institute of TechnologyXuzhouPeople’s Republic of China

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