Open Access

Norm equivalence and composition operators between Bloch/Lipschitz spaces of the ball

Journal of Inequalities and Applications20062006:61018

https://doi.org/10.1155/JIA/2006/61018

Received: 11 October 2005

Accepted: 12 February 2006

Published: 27 June 2006

Abstract

For , let and denote, respectively, the -Bloch and holomorphic -Lipschitz spaces of the open unit ball in . It is known that and are equal as sets when . We prove that these spaces are additionally norm-equivalent, thus extending known results for and the polydisk. As an application, we generalize work by Madigan on the disk by investigating boundedness of the composition operator from to .

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Authors’ Affiliations

(1)
Department of Mathematics, University of California
(2)
Mathematical Institute of the Serbian Academy of Science

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Copyright

© D. D. Clahane and S. Stević 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.