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Radial variation of analytic functions with non-tangential boundary limits almost everywhere

Published online by Cambridge University Press:  24 October 2008

D. J. Hallenbeck  and
K. Samotij
D. J. Hallenbeck
Affiliation:
Department of Mathematical Sciences, University of Delaware, Newark, Delaware 19716, U.S.A.
K. Samotij
Affiliation:
Instytut Matematyki, Politechniki Wrocławskiej, Wybrzeże St. Wyspiańskiego 27, 50-370 Wroclaw, Poland
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Extract

The purpose of this paper is to investigate the asymptotic behaviour as r → 1− of the integrals

and f is an analytic function on the unit disk Δ which has non-tangential limits at almost every point on ∂Δ. The paper is divided into three parts. In the first part we consider the case where λ ≠ 1/k, in the second the somewhat more delicate case when λ = 1/k and in the third part we concentrate on some problems related to the case λ = k = 1.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 108 , Issue 2 , September 1990 , pp. 371 - 379
Copyright
Copyright © Cambridge Philosophical Society 1990

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References

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