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ON THE HOLLAND–WALSH CHARACTERIZATION OF BLOCH FUNCTIONS

Published online by Cambridge University Press:  28 July 2008

Miroslav Pavlović
Miroslav Pavlović
Affiliation:
Faculty of Mathematics, University of Belgrade, Studentski trg 16, 11001 Belgrade, PP 550, Serbia ([email protected])
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Abstract

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It is proved that the Bloch norm of an arbitrary $C^1$-function defined on the unit ball $\mathbb{B}_n\subset\mathbb{R}^n$ is equal to

$$ \sup_{x,y\in\mathbb{B}_n,\,x\neq y}{(1-|x|^2)^{1/2}(1-|y|^2)^{1/2}}\frac{|f(x)-f(y)|}{|x-y|}. $$

Keywords

Primary 30D5546E15Bloch normholomorphic functionconformal automorphisms of the unit disc
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 51 , Issue 2 , June 2008 , pp. 439 - 441
Copyright
Copyright © Edinburgh Mathematical Society 2008