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An example of a non-exposed extreme function in the unit ball of H1

Published online by Cambridge University Press:  20 January 2009

Jyunji Inoue
Jyunji Inoue
Affiliation:
Department of Mathematics, Hokkaido University, Sapporo 060, Japan
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Abstract

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We construct a non-exposed extreme function f of the unit ball of H1, the classical Hardy space on the unit disc of the plane, which has the property: f(z)/(1−q(z))2 ∉ H1 for any nonconstant inner function q(z). This function constitutes a counterexample to a conjecture in D. Sarason [7].

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 37 , Issue 1 , February 1994 , pp. 47 - 51
Copyright
Copyright © Edinburgh Mathematical Society 1994

References

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