Composition operators in the Lipschitz Space of the Polydiscs

Zhongshan Fang, Zehua Zhou

Published 2007-09-10Version 1

In 1987, Shapiro shew that composition operator induced by symbol $\phi$ is compact on the Lipschltz space if and only if the infinity norm of $\phi$ is less than 1 by a spectral-theoretic argument, where $\phi$ is a holomorphic self-map of the unit disk. In this paper, we shall generalize Shapiro's result to the $n$-dimensional case.