Composition Operators from Hardy-Orlicz Spaces to Bloch-Orlicz Type Spaces
Received:September 28, 2017  Revised:June 16, 2018
Key Word: composition operator   Hardy-Orlicz space   Bloch-Orlicz space
Fund ProjectL:Supported by the National Natural Science Foundation of China (Grant No.11501130), the Natural Science Foundation of Guangdong Province (Grant No.2017A030310636) and the Science and Technology Project of Guangzhou City (Grant No.201707010126).
 Author Name Affiliation Zhonghua HE School of Financial Mathematics and Statistics, Guangdong University of Finance, Guangdong 510521, P. R. China
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Let $\varphi$ be an analytic self-map of $\mathbb{D}$. The composition operator $C_{\varphi}$ is the operator defined on $H(\mathbb{D})$ by $C_{\varphi}(f)=f\circ\varphi$. In this paper, we investigate the boundedness and compactness of the composition operator $C_{\varphi}$ from Hardy-Orlicz spaces to Bloch-Orlicz type spaces.