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Journal of Inequalities and Applications
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  • Research Article
  • Open Access

The essential norms of composition operators between generalized Bloch spaces in the polydisc and their applications

Journal of Inequalities and Applications20062006:90742

https://doi.org/10.1155/JIA/2006/90742

©  Z. Zhou and Y. Liu. 2006

  • Received: 27 December 2005
  • Accepted: 22 July 2006
  • Published:

Abstract

Let be the unit polydisc of and a holomorphic self-map of . , and denote the -Bloch space, little -Bloch space, and little star -Bloch space in the unit polydisc , respectively, where . This paper gives the estimates of the essential norms of bounded composition operators induced by between ( or ) and ( or ). As their applications, some necessary and sufficient conditions for the (bounded) composition operators to be compact from ( or ) into ( or ) are obtained.

Keywords

  • Composition Operator
  • Bloch Space
  • Essential Norm
  • Bound Composition Operator
  • Unit Polydisc

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Authors’ Affiliations

(1)
Department of Mathematics, Tianjin University, Tianjin, 300072, China

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Copyright

© Z. Zhou and Y. Liu. 2006

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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