Glasnik Matematicki, Vol. 34, No.2 (1999), 197-202.


Wei Xiao and Songping Zhou

Ningbo University, The Mathematical Institute, Ningbo, Zhejiang 315211, China

State Key Laboratory, Southwest Institute of Petroleum, Nanhchong, Sucian 637001, China

Abstract.   Let Hn be the class of real algebraic polynomials of degree n, whose zeros all lie in the interval [-1, 1]. Define || f || = max-1 ≤ x ≤ 1 | f(x)|. In 1939, Turan proved that for f Hn, || f ' || ≥ C√n || f ||. Usually, to establish weighted inequalities for polynomials requires more complicated techniques, especially in general cases. The object of this paper is to start the work in uniform norm under general requirements for weight functions.

1991 Mathematics Subject Classification.   26D10.

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