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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Subordination and $ H\sp p$ functions


Author: Rahman Younis
Journal: Proc. Amer. Math. Soc. 110 (1990), 653-660
MSC: Primary 30D55; Secondary 30C80
MathSciNet review: 1027103
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Abstract: Let $ \phi $ and $ W$ be inner functions with $ \phi (0) = W(0) = 0$. It is shown that if $ F$ is an exposed point of the unit ball of $ {H^1}$ and

$\displaystyle F(W({e^{it}}))/F(\phi ({e^{it}})) > 0$

almost everywhere, then $ F \circ W = F \circ \phi $. If $ f = zF$ such that $ F$ and $ 1/F$ are in $ {H^r}$ and $ {H^s}$, respectively, where $ 1/r + 1/s \leq 2$ and $ \phi $ is a finite Blaschke product, then a necessary and sufficient condition is provided in order for $ f(W({e^{it}}))/f(\phi ({e^{it}}))$ to be positive almost everywhere.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1990-1027103-9
PII: S 0002-9939(1990)1027103-9
Keywords: Exposed points, $ {H^p}$ functions, subordination
Article copyright: © Copyright 1990 American Mathematical Society