The sharp constant in Markov's inequality for the Laguerre weight

We prove that the polynomial of degree n that deviates least from zero in the uniformly weighted metric with Laguerre weight is the extremal polynomial in Markov's inequality for the norm of the kth derivative. Moreover, the corresponding sharp constant does not exceed (8k n ! k !)/((n-k)! (2k)!). For the derivative of a fixed order this bound is asymptotically sharp as n→∞. Bibliography: 20 items.