Hostname: page-component-586b7cd67f-dlnhk Total loading time: 0 Render date: 2024-12-01T00:04:28.484Z Has data issue: false hasContentIssue false
  • English
  • Français

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.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

1.Carleson, L., Selected Problems on Exceptional Sets (Van Nostrand, New York, 1967).Google Scholar
2.Hallenbeck, D. J. and MacGregor, T. H., Growth and zero sets of analytic families of Cauchy–Stieltjes integrals, J. Analyse Math., to appear.Google Scholar
3.Hallenbeck, D. J. and MacGregor, T. H., Radial limits and radial growth of Cauchy–Stieltjes transforms, Complex Variables 21 (1993), 219–229.Google Scholar
4.Twomey, J. B., Tangential boundary behavior of the Cauchy integral, J. London Math. Soc. 37 (1988), 447–454.CrossRefGoogle Scholar