Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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PRODUCT-TYPE OPERATORS FROM WEIGHTED BERGMAN-ORLICZ SPACES TO WEIGHTED ZYGMUND SPACES

  • JIANG, ZHI-JIE (INSTITUTE OF NONLINEAR SCIENCE AND ENGINEERING COMPUTING SICHUAN UNIVERSITY OF SCIENCE AND ENGINEERING)
  • Received : 2014.10.28
  • Published : 2015.07.31
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Abstract

Let ${\mathbb{D}}=\{z{\in}{\mathbb{C}}:{\mid}z{\mid}<1\}$ be the open unit disk in the complex plane $\mathbb{C}$, ${\varphi}$ an analytic self-map of $\mathbb{D}$ and ${\psi}$ an analytic function in $\mathbb{D}$. Let D be the differentiation operator and $W_{{\varphi},{\psi}}$ the weighted composition operator. The boundedness and compactness of the product-type operator $W_{{\varphi},{\psi}}D$ from the weighted Bergman-Orlicz space to the weighted Zygmund space on $\mathbb{D}$ are characterized.

Keywords

Acknowledgement

Supported by : National Natural Science Foundation of China

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