Norm Equivalence and Composition Operators between Bloch/lipschitz Spaces of the Ball

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