Hostname: page-component-5c6d5d7d68-lvtdw Total loading time: 0 Render date: 2024-08-06T22:21:46.206Z Has data issue: false hasContentIssue false
  • English
  • Français

Compact composition operators on Block spaces

Published online by Cambridge University Press:  17 April 2009

Chengji Xiong
Chengji Xiong
Affiliation:
Department of Mathematics, Nanjing Normal University, Nanjing 210097, China Department of Mathematics, Huaiyin Teachers' College, Huiayin 223001, China, e-mail: chengji_xiong@163.net
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The present paper proposes new criteria for compactness of a composition operator Cφf = f ∘ φ on the Bloch space and the little Bloch space. For the case when φ is univalent, a criterion given by K. Madigan and A. Matheson is generalised.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 68 , Issue 2 , October 2003 , pp. 185 - 190
Copyright
Copyright © Australian Mathematical Society 2003

References

[1]Anderson, J.M., Clunie, J. and Pomerenke, Ch., ‘On Bloch functions and normal functions’, J. Reine Angew.Math. 270 (1974), 12–37.Google Scholar
[2]Madigan, K. and Matheson, A., ‘Compact composition operators on Bloch space’, Trans. Amer. Math. Soc. 347 (1995), 2679–2687.CrossRefGoogle Scholar
[3]Pommerenke, Ch., Univalent functions (Vandenhoeck and Ruprecht, Göttingen, 1975).Google Scholar
[4]Pommerenke, Ch., Boundary behaviour of conformal maps (Springer-Verlag, Berlin, 1992).CrossRefGoogle Scholar