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.References
- Karel de Leeuw and Walter Rudin, Extreme points and extremum problems in $H_{1}$, Pacific J. Math. 8 (1958), 467–485. MR 98981, DOI 10.2140/pjm.1958.8.467
- J. Neuwirth and D. J. Newman, Positive $H^{1/2}$ functions are constants, Proc. Amer. Math. Soc. 18 (1967), 958. MR 213576, DOI 10.1090/S0002-9939-1967-0213576-5
- Walter Rudin, Function theory in polydiscs, W. A. Benjamin, Inc., New York-Amsterdam, 1969. MR 0255841
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