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A note on radial variation of analytic functions

Published online by Cambridge University Press:  26 February 2010

D. J. Hallenbeck  and
K. Samotij
D. J. Hallenbeck
Affiliation:
Professor D. J. Hallenbeck, Department of Mathematical Sciences, University of Delaware, Newark, Delaware 19716, U.S.A.
K. Samotij
Affiliation:
Dr. K. Samotij, Instytut Matematyki, Politechniki Wroclawskiej, Wybrzezé St. Wyspiánskjego 27, 50-370 Wroclaw, Poland.
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Abstract

Let F denote a family of analytic functions in the unit disk Δ. Suppose that one has a “sharp” estimate on the almost everywhere radial variation of functions in the class Δ. We prove that if Δ is contained in the Nevanlinna class N then the estimate will be “sharp” in the algebra A of functions analytic in Δ and continuous in Δ.

Type
Research Article
Information
Mathematika , Volume 38 , Issue 1 , June 1991 , pp. 191 - 193
Copyright
Copyright © University College London 1991

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References

1. Hallenbeck, D. J. and Samotij, K.. On radial variation of bounded analytic functions. Complex Variables, 15 (1990), 43–52.Google Scholar
2. Hallenbeck, D. J. and Samotij, K.. Radial variation of analytic functions with nontangential boundary limits almost everywhere. Math. Proc. Comb. Phil. Soc, 108 (1990), 371–379.CrossRefGoogle Scholar
3. Rudin, W.. The radial variation of analytic functions. Duke Math. J., 22 (1955), 235–242.CrossRefGoogle Scholar
4. Zygmund, A.. On certain integrals. Trans. Amer. Math. Soc, 55 (1944), 170–204.CrossRefGoogle Scholar
5. Zygmund, A.. Trigonometric Series, Vol. 1, 2nd ed. (Cambridge Univ. Press, London and New York, 1968).Google Scholar