Journal of Inequalities and Applications 
Volume 2006 (2006), Article ID 61018, 11 pages
doi:10.1155/JIA/2006/61018

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

Abstract

For p>0, let ℬp(Bn) and ℒp(Bn) denote, respectively, the p-Bloch and holomorphic p-Lipschitz spaces of the open unit ball Bn in ℂn. It is known that ℬp(Bn) and ℒ1−p(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 ℭφ from ℒp(Bn) to ℒq(Bn).