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- 주제어 : Loo-Keng Hua domain (검색결과 2 건)
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WEIGHTED COMPOSITION OPERATORS ON BERS-TYPE SPACES OF LOO-KENG HUA DOMAINS
Jiang, Zhi-jie,Li, Zuo-an Korean Mathematical Society 2020 대한수학회보 Vol.57 No.3
Let HE<sub>I</sub>, HE<sub>II</sub>, HE<sub>III</sub> and HE<sub>IV</sub> be the first, second, third and fourth type Loo-Keng Hua domain respectively, 𝜑 a holomorphic self-map of HE<sub>I</sub>, HE<sub>II</sub>, HE<sub>III</sub>, or HE<sub>IV</sub> and u ∈ H(𝓜) the space of all holomorphic functions on 𝓜 ∈ {HE<sub>I</sub>, HE<sub>II</sub>, HE<sub>III</sub>, HE<sub>IV</sub>}. In this paper, motivated by the well known Hua's matrix inequality, first some inequalities for the points in the Bers-type spaces of the Loo-Keng Hua domains are obtained, and then the boundedness and compactness of the weighted composition operators W<sub>𝜑,u</sub> : f ↦ u · f ◦ 𝜑 on Bers-type spaces of these domains are characterized.
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Weighted composition operators on Bers-type spaces of Loo-Keng Hua domains
Zhi-Jie Jiang,Zuo-an Li 대한수학회 2020 대한수학회보 Vol.57 No.3
Let $\mbox{HE}_I$, $\mbox{HE}_{II}$, $\mbox{HE}_{III}$ and $\mbox{HE}_{IV}$ be the first, second, third and fourth type Loo-Keng Hua domain respectively, $\vp$ a holomorphic self-map of $\mbox{HE}_I$, $\mbox{HE}_{II}$, $\mbox{HE}_{III}$, or $\mbox{HE}_{IV}$ and $u\in H(\M)$ the space of all holomorphic functions on $\M\in\{\mbox{HE}_I, \mbox{HE}_{II}, \mbox{HE}_{III}, \mbox{HE}_{IV}\}$. In this paper, motivated by the well known Hua's matrix inequality, first some inequalities for the points in the Bers-type spaces of the Loo-Keng Hua domains are obtained, and then the boundedness and compactness of the weighted composition operators $W_{\vp,u}:f\mapsto u\cdot f\circ\vp$ on Bers-type spaces of these domains are characterized.
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