On Stevi? Type Operator from \(H^\infty \) Space to the Logarithmic Bloch Sp

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• 作者：Yanyan Yu ; Yongmin Liu
• 关键词：$$H^\infty $$ H ∞space ; Logarithmic Bloch space ; Multiplication operator ; Composition operator ; Differentiation operator ; Primary 47B38 ; 47B33 ; Secondary 46E15 ; 30H05
• 刊名：Complex Analysis and Operator Theory
• 出版年：2015
• 出版时间：December 2015
• 年：2015
• 卷：9
• 期：8
• 页码：1759-1780
• 全文大小：563 KB
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• 作者单位：Yanyan Yu (1)
  Yongmin Liu (2)
  
  1. School of Mathematics and Physics Science, Xuzhou Institute of Technology, Xuzhou, 221000, People’s Republic of China
  2. School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou, 221116, People’s Republic of China
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Operator Theory
  Analysis
  
• 出版者：Birkh盲user Basel
• ISSN：1661-8262

文摘

Let \(H({\mathbb {D}})\) denote the space of all analytic functions on the unit disc \({\mathbb {D}}\) of the complex plane \( {\mathbb {C}}\), \(\psi _1,\psi _2\in H({\mathbb {D}})\), and \(\varphi \) be an analytic self-map of \( {\mathbb {D}}\). In this paper, we characterize the boundedness and compactness of Stevi? type operator \(T _{\psi _1,\psi _2,\varphi }\) from \(H^\infty \) space to the logarithmic Bloch spaces \({\mathcal {B}}_{\log }\) (\({\mathcal {B}}_{\log ,0}\)). Keywords \(H^\infty \) space Logarithmic Bloch space Multiplication operator Composition operator Differentiation operator