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Open Access

An Estimate of the Essential Norm of a Composition Operator from to in the Unit Ball

Journal of Inequalities and Applications20102010:132970

https://doi.org/10.1155/2010/132970

Received: 29 June 2009

Accepted: 17 February 2010

Published: 2 March 2010

Abstract

Let be the unit ball of and a holomorphic self-map of Let , , , , and let be the composition operator between the space and -Bloch space induced by . This paper gives an estimate of the essential norm of . As a consequence, a necessary and sufficient condition for the composition operator to be compact from to is obtained.

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Authors’ Affiliations

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

Copyright

© Zeng and Zhou. 2010

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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