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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Unicity of the extremum problems in $H^{1} (U^{n})$
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by Kôzô Yabuta PDF
Proc. Amer. Math. Soc. 28 (1971), 181-184 Request permission

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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Additional Information
  • © Copyright 1971 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 28 (1971), 181-184
  • MSC: Primary 32.12
  • DOI: https://doi.org/10.1090/S0002-9939-1971-0273053-3
  • MathSciNet review: 0273053