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Radial growth and variation of bounded analytic functions
Published online by Cambridge University Press: 13 July 2011
Extract
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.
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- Research Article
- Information
- Proceedings of the Edinburgh Mathematical Society , Volume 31 , Issue 3 , October 1988 , pp. 489 - 498
- Copyright
- Copyright © Edinburgh Mathematical Society 1988
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