Weighted Composition Operators from the Bloch Spaces to Weighted Hardy Spaces on Bounded Symmetric Domains

Abstract

Let $\mathbb{B}_{E}$ be a bounded symmetric domain realized as the unit open ball of JB*-triples. The authors will characterize the bounded weighted composition operator from the Bloch space $\cal{B}(\mathbb{B}_{E})$ to weighted Hardy space $H_{v}^{\infty}(\mathbb{B}_{E})$ in terms of Kobayashi distance. The authors also give a sufficient condition for the compactness, and also give the upper bound of its essential norm. As a corollary, they show that the boundedness and compactness are equivalent for composition operator from $\cal{B}(\mathbb{B}_{E})$ to $H^{\infty}(\mathbb{B}_{E})$, when E is a finite dimension JB*-triple. Finally, they show the boundedness and compactness of weighted composition operators from $H_{v}^{\infty}(\mathbb{B}_{E})$ to $H_{v,0}^{\infty}(\mathbb{B}_{E})$ are equivalent when E is a finite dimension JB*-triple.

Keywords

Weighted composition operators / Bloch functions / Holomorphic functions / Bounded symmetric domains / Kobayashi distance

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