Geodesic
Sharp Markov brothers type inequality in the spaces $L_p$, $L_1$ on a~closed interval
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 17 (2011) no. 3, pp. 282-290

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We study an inequality between the $L_p$-mean of the $(n-1)$th derivative of an algebraic polynomial of degree $n\geq2$ and the $L_1$-mean of this polynomial on a closed interval. Sharp constants and extremal polynomials are written for all $p\in[0,\infty]$.
Mots-clés : algebraic polynomial
Keywords: Markov type inequalities, Nikolskii type inequalities. 
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     author = {I. E. Simonov},
     title = {Sharp {Markov} brothers type inequality in the spaces $L_p$, $L_1$ on a~closed interval},
     journal = {Trudy Instituta matematiki i mehaniki},
     pages = {282--290},
     publisher = {mathdoc},
     volume = {17},
     number = {3},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMM_2011_17_3_a27/}
}
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I. E. Simonov. Sharp Markov brothers type inequality in the spaces $L_p$, $L_1$ on a~closed interval. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 17 (2011) no. 3, pp. 282-290. http://geodesic.mathdoc.fr/item/TIMM_2011_17_3_a27/