Sharp Markov brothers type inequality in the spaces L (p) and L (1) on a closed interval

Abstract

We study an inequality between the L p-mean of the (n - 1)th derivative of an algebraic polynomial of degree n ≥ 2 and the L 1-mean of this polynomial on a closed interval. Sharp constants and extremal polynomials are written for all p ∈ [0,∞]. © 2012 Pleiades Publishing, Ltd.