Compact Composition Operators on the Bloch Space in Bounded Symmetric Domains

Abstract

Let $\Omega$ be a bounded symmetric domain except the two exceptional domains of ${\mathbb{C}}^N$ and $\varphi$ a holomorphic self-map of $\Omega .$ This paper gives a sufficient and necessary condition for the composition operator $C_{\varphi }$ induced by $\varphi$ to be compact on the Bloch space $\beta (\Omega )$.

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