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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1981-0619992-9
PII: S 0002-9939(1981)0619992-9
Keywords: Bernstein's theorem, polynomial, the unit ball in several complex variables
Article copyright: © Copyright 1981 American Mathematical Society