Sharp constants in V. A. Markov–Bernstein type inequalities of different metrics

Abstract

We study relations between sharp constants in the V. A. Markov–Bernstein inequalities of different Lr-metrics for algebraic polynomials on an interval and for entire functions on the real line or half-line. In a number of cases, we prove that the sharp constant in the inequality for entire functions of exponential type or semitype is the limit of sharp constants in the corresponding inequalities for algebraic polynomials of degree n as n→∞.