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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

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