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

作者：Clahane Dana D^*; Stevic Stevo

来源：Journal of Inequalities and Applications, 2006, 61018.

DOI：10.1155/JIA/2006/61018

For p > 0, let B-p(B-n) and L-p(B-n) denote, respectively, the p-Bloch and holomorphic p-Lipschitz spaces of the open unit ball B-n in C-n. It is known that R-p(B-n) and L1-p(B-n) are equal as sets when p is an element of (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 C-phi from L-p(B-n) to L-q(B-n). Copyright (C) 2006 D. D. Clahane and S. Stevic. 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.

• 出版日期2006