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A uniqueness set for all Hp(Bn) with p>0

Published online by Cambridge University Press:  09 April 2009

P. S. Chee
P. S. Chee
Affiliation:
Department of Methematics University of MalayaKuala LumpurMalaysia
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Abstract

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For n≥2, a hypersurface in the open unit ball Bn in is constructed which satisfies the generalized Blaschke condition and is a uniqueness set for all Hp(Bn) with p>0. If n≥3, the hypersurface can be chosen to have finite area.

Subject classification (Amer. Math. Soc. (MOS) 1970): primary 32 A 10.

Keywords

BallsNevanlinna classHardy spaceszero setsuniqueness setsBlaschke conditionhypersurfaces
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 26 , Issue 1 , August 1978 , pp. 65 - 69
Copyright
Copyright © Australian Mathematical Society 1978

References

Chee, P. S. (1970a), “The Blaschke condition for bounded holomorphic functions”, Trans. Amer. Math. Soc. 148, 249–263.CrossRefGoogle Scholar
Chee, P. S. (1970b), “On the generalized Blaschke condition”, Trans. Amer. Math. Soc. 152, 227–231.CrossRefGoogle Scholar
Miles, J. (1973), “Zero sets in Hp(Un)”, Illinois J. Math. 17, 458–464.Google Scholar
Rudin, W. (1976), “Zeros of holomorphic functions in balls”, Indag. Math. 38, 57–65.CrossRefGoogle Scholar