Norm Equivalence and Composition Operators on Bloch/Lipschitz spaces of the Unit Ball
Complex Variables
2007-05-23 v3 Functional Analysis
Abstract
When 0<p<1, it is known that the p-Bloch and (1-p)-Lipschitz spaces of the unit ball in n-dimensional complex Eucllidean space are equal as sets. 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 composition operators between p- and q-Lipschitz spaces of the ball.
Cite
@article{arxiv.math/0506424,
title = {Norm Equivalence and Composition Operators on Bloch/Lipschitz spaces of the Unit Ball},
author = {Dana D. Clahane and Stevo Stevic},
journal= {arXiv preprint arXiv:math/0506424},
year = {2007}
}
Comments
11 pages (minor expositional changes and typographical errors made based on a referee's comments)