Hostname: page-component-8448b6f56d-tj2md Total loading time: 0 Render date: 2024-04-19T06:57:50.735Z Has data issue: false hasContentIssue false

Norm of composition operators on the Bloch space

Published online by Cambridge University Press:  17 April 2009

Chengji Xiong
Affiliation:
Department of Mathematics, Shantou University, Shantou, Guangdong 515063, Peoples Republic of China Department of Mathematics, Huaiyin Teacher's College, Huaiyin, Jiangsu 223001, Peoples Republic of China e-mail: chengji_xiong@yahoo.com
Rights & Permissions [Opens in a new window]

Extract

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 author estimates the semi-norm and norm of composition operators on the Block space; and obtains several necessary conditions for a composition operator to be isometric.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 2004

References

[1]Anderson, J.M., Clunie, J. and Pomerenke, Ch., ‘On Bloch functions and normal functions’, J. Reine Angew. Math. 270 (1974), 1237.Google Scholar
[2]Littlewood, J.E., ‘On inequalities in the theory of functions’, Proc. London Math. Soc. 23 (1925), 481519.CrossRefGoogle Scholar
[3]Nordgren, E.A., ‘Composition operators’, Canad, J. Math. 20 (1968), 442449.Google Scholar
[4]Madigan, K. and Matheson, A., ‘Compact composition operators on Bloch space’, Trans. Amer. Math. Soc. 347 (1995), 26792687.Google Scholar
[5]Shapiro, J.H., ‘What do composition operators know about inner functions?’, Monatshefte für Mathematik 130 (2000), 5770.Google Scholar
[6]Shapiro, J.H., Composition operators and classical function theory (Springer-Verlag, New York, 1993), pp. 5560.Google Scholar