Journal of Inequalities and Applications
Volume 2006 (2006), Article ID 61018, 11 pages

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

Dana D. Clahane1 and Stevo Stević2

1Department of Mathematics, University of California, Riverside 92521, CA, USA
2Mathematical Institute of the Serbian Academy of Science, Knez Mihailova 35/I, Beograd 11000, Serbia

Received 11 October 2005; Revised 30 January 2006; Accepted 12 February 2006

Copyright © 2006 Dana D. Clahane and Stevo Stević. 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.


For p>0, let p(Bn) and p(Bn) denote, respectively, the p-Bloch and holomorphic p-Lipschitz spaces of the open unit ball Bn in n. It is known that p(Bn) and 1p(Bn) are equal as sets when p(0,1). We prove that these spaces are additionally norm-equivalent, thus extending known results for n=1 and the polydisk. As an application, we generalize work by Madigan on the disk by investigating boundedness of the composition operator φ from p(Bn) to q(Bn).