Product-type operators from weighted Bergman-Orlicz spaces to weighted Zygmund spaces
Bull. Korean Math. Soc. 2015 Vol. 52, No. 4, 1383-1399
Printed July 31, 2015
Zhi-Jie Jiang
Sichuan University of Science and Engineering
Abstract : Let $\DD=\{z\in\C:|z|<1\}$ be the open unit disk in the complex plane $\C$, $\vp$ an analytic self-map of $\DD$ and $\psi$ an analytic function in $\DD$. Let $D$ be the differentiation operator and $W_{\vp,\psi}$ the weighted composition operator. The boundedness and compactness of the product-type operator $W_{\vp,\psi}D$ from the weighted Bergman-Orlicz space to the weighted Zygmund space on $\DD$ are characterized.
Keywords : weighted Bergman-Orlicz spaces, product-type operators, weight\-ed Zygmund spaces, boundedness, compactness
MSC numbers : Primary 47B38; Secondary 47B33, 47B37
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