Composition operators in the Lipschitz Space of the Polydiscs

Details Composition operators in the Lipschitz Space of the Polydiscs Composition operators in the Lipschitz Space of the Polydiscs

2007-09-10

arxiv.org/abs/0709.1435v1

Mathematics

Functional Analysis

7 pages

Scientific paper

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.

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