Proceedings of the Edinburgh Mathematical Society (Series 2)

Table of Contents - October 1988 - Volume 31, Issue 03  

Research Article

Radial growth and variation of bounded analytic functions

D. J. Hallenbecka1 and T. H. MacGregora2

a1 Department of Mathematical Sciences University of Delaware Newark, Delaware 19716, U.S.A.

a2 Department of Mathematics and Statistics SUNY at Albany 1400 Washington Avenue Albany, New York 12222, U.S.A.

If a function f analytic in Δ = {zxs2208xs2102:|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.

(Received March 17 1987)