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Complex Variables and Elliptic Equations
An International Journal
Volume 52, 2007 - Issue 10-11: A Tribute to Jianke Lu
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Original Articles

Closed range composition operators on the Bloch space in the unit ball of ℂn

Fangwen Deng Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan, 430071, China
,
Liangying Jiang Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan, 430071, China
&
Caiheng Ouyang Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan, 430071, ChinaCorrespondence[email protected]
Pages 1029-1037 | Accepted 13 Jul 2007, Published online: 22 Sep 2010
 
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Abstract

In this article, we give some necessary conditions and sufficient conditions for a composition operator C ϕ on the Bloch space to have closed range, in which the necessity is connected with the sampling set induced by the Bergman metric and the automorphism-invariant distance of the ball; and the sufficiency with the sampling set induced by complex Jacobian of holomorphic self-map ϕ and the reverse Carleson condition, respectively.

†Dedicated to Professor Jianke Lu for his 85th birthday.

AMS Subject Classifications::

Acknowledgements

Supported in part by the National Natural Science Foundation of China (Nos. 10571044 and 10401027).

Notes

†Dedicated to Professor Jianke Lu for his 85th birthday.

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