On the best constants in inequalities of the Markov and Wirtinger types for polynomials on the half-line

Abstract

The main topic of the paper is best constants in Markov-type inequalities between the norms of higher derivatives of polynomials and the norms of the polynomials themselves. The norm is the L2 norm with Laguerre weight. The leading term of the asymptotics of the constants is determined and tight bounds for the principal coefficient in this term, which is the operator norm of a Volterra operator, are given. For best constants in inequalities of the Wirtinger type, the limit is computed and an asymptotic formula for the error term is presented. © 2008 Elsevier Inc. All rights reserved.