Composition operators in the Lipschitz Space of the Polydiscs

Abstract

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

7 pages

References in corpus (1)

• The Essential Norm of Composition Operator between Generalized Bloch Spaces in Polydiscs and its Applications