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Proceedings of the American Mathematical Society

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Extension of Bernšteĭn's theorem

Author: S. H. Tung
Journal: Proc. Amer. Math. Soc. 83 (1981), 103-106
MSC: Primary 32A15; Secondary 30E10, 32A30
MathSciNet review: 619992
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Abstract: A well-known theorem of Bernstein states that if a polynomial of degree $ n$ of a complex variable has its modulus no larger than one on the unit disk then the modulus of its derivative will not exceed $ n$ on the unit disk. Here we extend the theorem to polynomials on the unit ball in several complex variables.

References [Enhancements On Off] (What's this?)

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Keywords: Bernstein's theorem, polynomial, the unit ball in several complex variables
Article copyright: © Copyright 1981 American Mathematical Society