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Radial growth and exceptional sets for Cauchy–Stieltjes integrals
Published online by Cambridge University Press: 20 January 2009
Abstract
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
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