Journal of Inequalities and Applications
Volume 2009 (2009), Article ID 808720, 8 pages
doi:10.1155/2009/808720
Research Article

Markov Inequalities for Polynomials with Restricted Coefficients

Feilong Cao1 and Shaobo Lin2

1Department of Information and Mathematics Sciences, China Jiliang University, Hangzhou 310018, Zhejiang Province, China
2Department of Mathematics, Hangzhou Normal University, Hangzhou 310018, Zhejiang Province, China

Received 13 November 2008; Revised 6 February 2009; Accepted 15 April 2009

Academic Editor: Siegfried Carl

Copyright © 2009 Feilong Cao and Shaobo Lin. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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)=∑k=hnakxk, ak∈ℤ, |ak|≤nδ, |ah|=max⁡h≤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 cδnlog⁡(n+1) for polynomials in the classes ℱn,δ on [0,1].