PRODUCT-TYPE OPERATORS FROM WEIGHTED BERGMAN-ORLICZ SPACES TO WEIGHTED ZYGMUND SPACES

Title & Authors
PRODUCT-TYPE OPERATORS FROM WEIGHTED BERGMAN-ORLICZ SPACES TO WEIGHTED ZYGMUND SPACES
JIANG, ZHI-JIE;

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