Markov Inequalities for Polynomials with Restricted Coefficients
نویسندگان
چکیده
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 Fn,δ as the collection of all polynomials of the form P x ∑n k h akx k , ak ∈ Z, |ak | ≤ n , |ah| maxh≤k≤n|ak |. In this paper, we prove essentially sharp Markov-type inequalities for polynomials from the classes Fn,δ on 0, 1 . Our main result shows that the Markov factor 2n2 valid for all polynomials of degree at most n on 0, 1 improves to cδn log n 1 for polynomials in the classes Fn,δ on 0, 1 .
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