Hostname: page-component-848d4c4894-75dct Total loading time: 0 Render date: 2024-06-03T22:33:34.454Z Has data issue: false hasContentIssue false
  • English
  • Français

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
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.

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

REFERENCES

1.Duren, P. L., Theory of HP spaces (Academic Press Inc., New York and London 1970).Google Scholar
2.DeLeeuw, K. and Rudin, W., Extreme points and extremum problems in H 1, Pacific J. Math. 8 (1958), 467–485.CrossRefGoogle Scholar
3.Hayashi, E., Solution sets of extremal problems in H 1, Proc. Amer. Math. Soc. 93 (1985), 690–696.Google Scholar
4.Helson, H., Large analytic functions II, in Analysis and Partial Differential Equations (ed. Sadosky, Cora, Marcel Dekker, 1990), 217–220.Google Scholar
5.Koosis, P., Introduction of H1 spaces (Cambridge University Press, 1980).Google Scholar
6.Nakazi, T., Sum of two inner functions and exposed points in H 1, Proc. Edinburgh Math. Soc. 35 (1992), 349–357.CrossRefGoogle Scholar
7.Sarason, D., Exposed points in H 1, I, Oper. Theory Adv. Appl. 41 (1989), 485–496.Google Scholar