Geodesic
A Sharp Markov Brothers-Type Inequality in the Spaces~$L_\infty$ and $L_1$ on the Segment
Matematičeskie zametki, Tome 93 (2013) no. 4, pp. 604-613

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The inequality between the uniform norm of the derivative of order $\ell$ of an algebraic polynomial of degree $n$ and the $L_1$-norm of the polynomial itself on a segment are studied. For all $\ell\ge(n-1)/3$, the exact constant and the extremal polynomial are written out.
Keywords: Markov brothers' inequality, trigonometric polynomial, Chebyshev polynomial
Mots-clés : algebraic polynomial, Legendre polynomial. 
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     author = {I. E. Simonov},
     title = {A {Sharp} {Markov} {Brothers-Type} {Inequality} in the {Spaces~}$L_\infty$ and $L_1$ on the {Segment}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {604--613},
     publisher = {mathdoc},
     volume = {93},
     number = {4},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2013_93_4_a10/}
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I. E. Simonov. A Sharp Markov Brothers-Type Inequality in the Spaces~$L_\infty$ and $L_1$ on the Segment. Matematičeskie zametki, Tome 93 (2013) no. 4, pp. 604-613. http://geodesic.mathdoc.fr/item/MZM_2013_93_4_a10/