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RADIAL BEHAVIOUR OF INNER FUNCTIONS IN [Bscr ]0

Published online by Cambridge University Press:  19 March 2001

J. J. DONAIRE
J. J. DONAIRE
Affiliation:
Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra (Barcelona), Spain; [email protected]
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Abstract

With probabilistic techniques, it is proved that an inner function in the little Bloch space can have every asymptotic radial behaviour on sets of Hausdorff dimension 1. This is applied to deduce some differentiability properties of positive singular smooth measures and a result on radial cluster set interpolation for inner functions.

Type
Research Article
Information
Journal of the London Mathematical Society , Volume 63 , Issue 1 , February 2001 , pp. 141 - 158
Copyright
The London Mathematical Society 2001

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Footnotes

This work is partially supported by grants PB-95-0956-C02-02 (Ministerio de Educación y Cultura) and 1998SGR-00052 (Generalitat de Catalunya).