Sharp Markov-Nikol'skii inequality with respect to the uniform norm and the integral norm with Chebyshev weight

We study the inequality between the uniform norm of the derivative of an algebraic polynomial of degree n and the integral norm of this polynomial with Chebyshev weight on a closed interval. We found exact constants and extremal polynomials for derivatives of any order. © 2014 Elsevier Inc.The authors would like to thank the referees for reading the paper carefully and valuable comments. This work was supported by the Program for State Support of Leading Universities of the Russian Federation (agreement no. 02.A03.21.0006 of August 27, 2013)