Markov Inequalities for Polynomials with Restricted Coefficients

Feilong Cao, Shaobo Lin
2009 Journal of Inequalities and Applications  
Essentially sharp Markov-type inequalities are known for various classes of polynomials with constraints including constraints of the coefficients of the polynomials. For N and δ > 0 we introduce the class F n,δ as the collection of all polynomials of the form P x n k h a k x k , a k ∈ Z, |a k | ≤ n δ , |a h | max h≤k≤n |a k |. In this paper, we prove essentially sharp Markov-type inequalities for polynomials from the classes F n,δ on 0, 1 . Our main result shows that the Markov factor 2n 2
more » ... d for all polynomials of degree at most n on 0, 1 improves to c δ n log n 1 for polynomials in the classes F n,δ on 0, 1 .
doi:10.1155/2009/808720 fatcat:kmpnk4nenvhkzpnk6zkgqkafva