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Boundedness from Below of Composition Operators on α-Bloch Spaces

Published online by Cambridge University Press:  20 November 2018

Huaihui Chen  and
Paul Gauthier
Huaihui Chen
Affiliation:
Department of Mathematics, Nanjing Normal University, Nanjing 210097, P. R. China e-mail: [email protected]
Paul Gauthier
Affiliation:
Mathématiques et Statistique, CP-6128 Centre Ville, Université de Montréal, Montréal, PQ, H3C3J7 e-mail: [email protected]
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Abstract

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We give a necessary and sufficient condition for a composition operator on an $\alpha$-Bloch space with $\alpha \,\ge \,1$ to be bounded below. This extends a known result for the Bloch space due to P. Ghatage, J. Yan, D. Zheng, and H. Chen.

Keywords

32A1830H05Bloch functionscomposition operators
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 51 , Issue 2 , 01 June 2008 , pp. 195 - 204
Copyright
Copyright © Canadian Mathematical Society 2008

References

[1] Ahlfors, L. V., Conformal Invariants Topics in Geometric Function Theory. McGraw-Hill, New York, 1973.Google Scholar
[2] Anderson, J. M., Clunie, J., and Pommerenke, C., On Bloch functions and normal functions. J. Reine Angew. Math. 240(1974), 12–37.Google Scholar
[3] Chen, H., Boundedness from below of composition operators on the Bloch spaces, Science in China, Ser. A 46 (2003), no. 6, 838–946.Google Scholar
[4] Ghatage, P., Yan, J., and Zheng, D., Composition operators with closed range on the Bloch space. Proc. Amer. Math. Soc. 129(2000), no. 6, 2039–2044.Google Scholar
[5] Ghatage, P., Zheng, D., and Zorboska, N., Sampling sets and closed range composition operators on the Bloch space. Proc. Amer. Math. Soc. 133(2005), 1371–1377.Google Scholar
[6] Zhu, K., Bloch type spaces of analytic functions. Rocky Mountain J. Math. 23(1993), 1143–1177.Google Scholar