Asymptotically sharp Markov and Schur inequalities on general sets

Abstract

Markov's inequality for algebraic polynomials on $\left[-1,1\right]$ goes back to more than a century and it is widely used in approximation theory. Its asymptotically sharp form for unions of finitely many intervals has been found only in 2001 by the third author. In this paper we extend this asymptotic form to arbitrary compact subsets of the real line satisfying an interval condition. With the same method a sharp local version of Schur's inequality is given for such sets.