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A criterion for normality of analytic mappings
Part of:
Entire and meromorphic functions, and related topics
Spaces and algebras of analytic functions
Holomorphic functions of several complex variables
Published online by Cambridge University Press: 19 November 2021
Abstract
In this paper, we give a generalization and improvement of the Pavlović result on the characterization of continuously differentiable functions in the Bloch space on the unit ball in $\mathbb {R}^{m}$. Then, we derive a Holland–Walsh type theorem for analytic normal mappings on the unit disk.
Keywords
MSC classification
- Type
- Research Article
- Information
- Proceedings of the Edinburgh Mathematical Society , Volume 65 , Issue 1 , February 2022 , pp. 80 - 88
- Copyright
- Copyright © The Author(s), 2021. Published by Cambridge University Press on Behalf of The Edinburgh Mathematical Society
References
Anderson, J., Clunie, J. and Pommerenke, Ch., On Bloch functions and normal functions, J. die reine und angewandte Math. 270 (1974), 12–37.Google Scholar
Colonna, F., Bloch and normal functions and their relation, Rendiconti del Circolo Matematico di Palermo Series 2 38 (1989), 161–180.CrossRefGoogle Scholar
Colonna, F., The Bloch constant of bounded harmonic mappings, Indiana Univ. Math. J. 38 (1989), 829–840.CrossRefGoogle Scholar
Holland, F. and Walsh, D., Criteria for membership of Bloch space and its subspace, BMOA, Math. Ann. 273 (1986), 317–335.CrossRefGoogle Scholar
Marković, M., Differential-free characterisation of smooth mappings with given growth, Canad. Math. Bull. 61 (2018), 628–636.CrossRefGoogle Scholar
Pavlović, M., On the Holland–Walsh characterization of Bloch functions, Proc. Edinburgh Math. Soc. 51 (2008), 439–441.CrossRefGoogle Scholar
Ren, G. and Kähler, U., Weighted Lipschitz continuity and harmonic Bloch and Besov spaces, Proc. Edinb. Math. Soc. 48 (2005), 743–755.CrossRefGoogle Scholar
Ren, G. and Tu, C., Bloch space in the unit ball of $\mathbb {C}^{n}$, Proc. Am. Math. Soc. 133 (2005), 719–726.CrossRefGoogle Scholar
Zhu, K., Distances and Banach spaces of holomorphic functions on complex domains, J. London Math. Soc. 49 (1994), 163–182.CrossRefGoogle Scholar