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 Bounded composition operators from the Bergman space to the Hardy space Bull. Korean Math. Soc. 2014 Vol. 51, No. 4, 1005-1013 https://doi.org/10.4134/BKMS.2014.51.4.1005Published online July 31, 2014 Kazuhiro Kasuga and Takahiko Nakazi Kogakuin University, Hokusei Gakuen University Abstract : Let $\phi$ be an analytic self map of the open unit disc $D$. In this paper, we study the composition operator $C_\phi$ from the Bergman space on $D$ to the Hardy space on $D$. Keywords : Bergman space, Hardy space, isometry, bounded composition, Nevanlinna counting function MSC numbers : 47B33 Full-Text :