A Sharp Inequality of Markov Type for Polynomials Associated with Laguerre Weight

Abstract

The best possible constant An in an inequality of Markov type [ddx(e−xpn(x))][0, ∞)⩽An‖e−xpn(x)‖[0, ∞), where ‖·‖[0, ∞) denotes the sup-norm on the half real line [0, ∞) and pn is an arbitrary polynomial of degree at most n, is determined in terms of the weighted Chebyshev polynomials associated with the Laguerre weight e−x on [0, ∞).