Compact composition operators on the Bloch space in polydiscs |
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Authors: | Zhou Zehua SHI Jihuai |
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Institution: | Department of Mathematics, University of Science and Technology of China, Hefei 230026, China |
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Abstract: | Let Un be the unit polydisc of ℂn and φ=(φ1, ⋯, φ
n
) a holomorphic self-map of Un. As the main result of the paper, it shows that the composition operator C is compact on the Bloch space β(Un) if and only if for every ε > 0, there exists a δ > 0, such that whenever dist(φ(z), ∂U
n
)<δ. |
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Keywords: | Bloch space polydisc composition operator Bergman mertic |
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