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UNIVERSAL RADIAL LIMITS OF HOLOMORPHIC FUNCTIONS

Published online by Cambridge University Press:  27 July 2005

FRÉDÉRIC BAYART
FRÉDÉRIC BAYART
Affiliation:
Laboratoire Bordelais d'Analyse et de Géométrie, UMR 5467, Université Bordeaux 1, 351 Cours de la Libération, F-33405 Talence cedex e-mail: bayart@math.u-bordeaux1.fr
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Abstract

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We investigate the radial behavior of holomorphic functions in the unit ball $B$ of $\mtc^n$. In particular, we prove the existence of universal holomorphic functions $f$ in the following sense : given any measurable function $\vphi$ on $\partial B$, there is a sequence $(r_n)_{n\geq 1}$, $0<r_n<1$, that converges to 1, such that $f(r_n\xi)$ converges to $\vphi(\xi)$ for almost every $\xi\,{\in}\,\partial B$.

Keywords

32A40
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 47 , Issue 2 , May 2005 , pp. 261 - 267
Copyright
2005 Glasgow Mathematical Journal Trust