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Radial growth and exceptional sets for Cauchy–Stieltjes integrals

Published online by Cambridge University Press:  20 January 2009

D. J. Hallenbeck  and
T. H. MacGregor
D. J. Hallenbeck
Affiliation:
Department of Mathematical Sciences, University of Delaware, Newark, Delaware 19716, U.S.A.
T. H. MacGregor
Affiliation:
Department of Mathematics and Statistics, Suny at Albany, 1400 Washington Avenue, Albany, New York 12222, U.S.A.
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Abstract

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This paper considers the radial and nontangential growth of a function f given by

where α>0 and μ is a complex-valued Borel measure on the unit circle. The main theorem shows how certain local conditions on μ near eiθ affect the growth of f(z) as z→eiθ in Stolz angles. This result leads to estimates on the nontangential growth of f where exceptional sets occur having zero β-capacity.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 37 , Issue 1 , February 1994 , pp. 73 - 89
Copyright
Copyright © Edinburgh Mathematical Society 1994

References

REFERENCES

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