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

Abstract

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 1-p ( Bn) are equal as sets when p∈( 0,1). We prove that these spaces are additionally norm-equivalent, thus extending known results for nCombining double low line1 and the polydisk. As an application, we generalize work by Madigan on the disk by investigating boundedness of the composition operator Cφ from p ( Bn) to q ( Bn).