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Radial growth and variation of bounded analytic functions

Published online by Cambridge University Press:  13 July 2011

D. J. Hallenbeck  and
T. H. MacGregor
D. J. Hallenbeck
Affiliation:
Department of Mathematical SciencesUniversity of DelawareNewark, Delaware 19716, U.S.A.
T. H. MacGregor
Affiliation:
Department of Mathematics and StatisticsSUNY at Albany1400 Washington AvenueAlbany, New York 12222, U.S.A.
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If a function f analytic in Δ = {z∈ℂ:|z|<1} has a nontangential limit as z→eiθ, then limr→1−(1−r)f′(reiθ)=0 [7, p. 181). It follows that this limit is zero for almost all θ for a number of classes of functions including the set H∞ of bounded analytic functions. In this paper we prove that this result for H∞ is sharp in a strong sense.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 31 , Issue 3 , October 1988 , pp. 489 - 498
Copyright
Copyright © Edinburgh Mathematical Society 1988

References

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