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arXiv · 0709.1435

Composition operators in the Lipschitz Space of the Polydiscs

Zhongshan Fang·Zehua Zhou
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Abstract

In 1987, Shapiro shew that composition operator induced by symbol $ϕ$ is compact on the Lipschltz space if and only if the infinity norm of $ϕ$ is less than 1 by a spectral-theoretic argument, where $ϕ$ 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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Zhongshan Fang, Zehua Zhou. 2007-09-10. Composition operators in the Lipschitz Space of the Polydiscs. https://arxiv.org/abs/0709.1435

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