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Proceedings of the American Mathematical Society

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$ H\sp 1$ subordination and extreme points


Author: Yusuf Abu-Muhanna
Journal: Proc. Amer. Math. Soc. 95 (1985), 247-251
MSC: Primary 30C80
MathSciNet review: 801332
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Abstract: Suppose that $ F$ is an element of $ {H^1}$ (Hardy class of order 1 over the unit disc). Let $ {\text{s}}(F)$ denote the set of functions subordinate to $ F$. We show that if $ \phi $ is inner and $ \phi (0) = 0$; then $ F \circ \phi $ is an extreme point of the closed convex hull of $ {\text{s}}(F)$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1985-0801332-7
Keywords: Extreme point, $ {H^p}$-functions, inner function, outer function subordination
Article copyright: © Copyright 1985 American Mathematical Society