Weighted Composition Operators from the Minimal M枚bius Invariant Space into the Bloch Space

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• 作者：Flavia Colonna (1)
  Songxiao Li (2)
  
• 关键词：Primary 47B33 ; Secondary 30H30 ; Weighted composition operator ; minimal m枚bius invariant space ; Bloch space
• 刊名：Mediterranean Journal of Mathematics
• 出版年：2013
• 出版时间：February 2013
• 年：2013
• 卷：10
• 期：1
• 页码：395-409
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• 作者单位：Flavia Colonna (1)
  Songxiao Li (2)
  
  1. Department of Mathematical Sciences, George Mason University, Fairfax, VA, 22030, U.S.A.
  2. Department of Mathematics, JiaYing University, 514015, Meizhou, GuangDong, China
  
• ISSN：1660-5454

文摘

Let ${{\varphi}}$ be an analytic self-map of the open unit disk ${{\mathbb{D}}}$ in the complex plane ${{\mathbb{C}, H(\mathbb{D})}}$ the space of complex-valued analytic functions on ${{\mathbb{D}}}$ , and let u be a fixed function in ${{H(\mathbb{D})}}$ . The weighted composition operator is defined by $$(uC_{\varphi}f)(z) = u(z)f({\varphi}(z)), \quad z \in \mathbb{D}, f \in H(\mathbb{D}).$$ In this paper, we study the boundedness and the compactness of the weighted composition operators from the minimal M枚bius invariant space into the Bloch space and the little Bloch space.