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An argument of a function in H1/2

Part of: Spaces and algebras of analytic functions

Published online by Cambridge University Press:  23 February 2012

Takahiko Nakazi  and
Takanori Yamamoto
Takahiko Nakazi
Affiliation:
School of Economics, Hokusei Gakuen University, Sapporo 004-8631, Japan ([email protected])
Takanori Yamamoto
Affiliation:
Department of Mathematics, Hokkai-Gakuen University, Sapporo 062-8605, Japan ([email protected])
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Abstract

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Let H1/2 be the Hardy space on the open unit disc. For two non-zero functions f and g in H1/2, we study the relation between f and g when f/g ≥ 0 a.e. on ∂D. Then we generalize a theorem of Neuwirth and Newman and Helson and Sarason with a simple proof.

Keywords

Hardy spaceargumentboundary value

MSC classification

Secondary: 30H10: Hardy spaces
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 55 , Issue 2 , June 2012 , pp. 507 - 511
Copyright
Copyright © Edinburgh Mathematical Society 2012

References

1.Helson, H., Large analytic functions, II, in Analysis and partial differential equations (ed. Sadosky, C.), Lecture Notes in Pure and Applied Mathematics, Volume 122, pp. 217–220 (Marcel Dekker, 1990).Google Scholar
2.Helson, H. and Sarason, D., Past and future, Math. Scand. 21 (1967), 5–16.CrossRefGoogle Scholar
3.Inoue, J. and Nakazi, T., Nonnegative functions in weighted Hardy spaces, Complex Variables 49 (2004), 837–843.Google Scholar
4.Nakazi, T., Functions in N + with the positive real parts on the boundary, and extremal problems in H 1, Complex Variables 44 (2001), 259–279.Google Scholar
5.Neuwirth, J. and Newman, D. J., Positive H 1/2 functions are constants, Proc. Am. Math. Soc. 18 (1967), 958.Google Scholar