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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Unicity of the extremum problems in $H^{1} (U^{n})$

Author: Kôzô Yabuta
Journal: Proc. Amer. Math. Soc. 28 (1971), 181-184
MSC: Primary 32.12
MathSciNet review: 0273053
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Abstract: In 1958 de Leeuw and Rudin have given a sufficient condition for a function in ${H^1}(U)$ to be a unique solution of the extremum problem. We give in this paper a stronger sufficient condition (Theorem 1) which holds also in $n$-dimension. Our Theorem 1 fills up considerably the gap of de Leeuw-Rudin’s result. We give also another proof of Neuwirth-Newman’s theorem and its $n$-dimensional generalization.

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Keywords: Hardy class, polydisc, extremum problem, extreme point, outer function, inner function, Poisson integral, homogeneous expansion
Article copyright: © Copyright 1971 American Mathematical Society