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Locally univalent functions, VMOA and the Dirichlet space

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Gallardo Gutiérrez, Eva A. and González, M. J. and Pérez González, Fernando and Pommerenke, Christian and Rattya, Jouni (2013) Locally univalent functions, VMOA and the Dirichlet space. Proceedings of the London Mathematical Society , 106 (Part 3). pp. 565-588. ISSN 0024-6115

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Official URL: http://plms.oxfordjournals.org/content/106/3/565.full.pdf+html


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Abstract

We study geometric properties of the image of the unit circle under a bounded locally univalent function g such that log g' belongs either to the Dirichlet space D, VMOA or the little Bloch space B-0. Concerning VMOA and B-0, our findings generalize the corresponding results for conformal maps shown by Pommerenke in the late 1970s. In the case of D, we give a strictly geometric necessary condition for g to satisfy log g'is an element of D, and also offer two different 'semi-geometric' characterizations of when log g'is an element of D.


Item Type:Article
Uncontrolled Keywords:Bounded mean oscillation; Schlicht functions; analytic-functions
Subjects:Sciences > Mathematics > Functions
ID Code:22152
Deposited On:28 Jun 2013 10:47
Last Modified:07 Feb 2014 10:42

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