Geodesic
The sharp constant in Markov's inequality for the Laguerre weight
Sbornik. Mathematics, Tome 200 (2009) no. 6, pp. 887-897

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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 $k$th derivative. Moreover, the corresponding sharp constant does not exceed $$ \frac{8^kn!\,k!}{(n-k)!\,(2k)!}. $$ For the derivative of a fixed order this bound is asymptotically sharp as $n\to\infty$. Bibliography: 20 items.
Keywords: Markov's inequality, weighted polynomial inequalities. 
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     author = {V. P. Sklyarov},
     title = {The sharp constant in {Markov's} inequality for the {Laguerre} weight},
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     number = {6},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2009_200_6_a3/}
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V. P. Sklyarov. The sharp constant in Markov's inequality for the Laguerre weight. Sbornik. Mathematics, Tome 200 (2009) no. 6, pp. 887-897. http://geodesic.mathdoc.fr/item/SM_2009_200_6_a3/