Geodesic
Estimating the $L_p$-norm of an algebraic polynomial in terms of its values at the nodes of a uniform grid
Sbornik. Mathematics, Tome 188 (1997) no. 12, pp. 1861-1884 
I. I. Sharapudinov. Estimating the $L_p$-norm of an algebraic polynomial in terms of its values at the nodes of a uniform grid. Sbornik. Mathematics, Tome 188 (1997) no. 12, pp. 1861-1884. http://geodesic.mathdoc.fr/item/SM_1997_188_12_a6/
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Voir la notice de l'article provenant de la source Math-Net.Ru

An estimate of the $L_p$-norm, $p\geqslant 1$, of an arbitrary algebraic polynomial of degree $\leqslant n$ in terms of its values at $N>n$ nodes of a uniform grid is obtained. This estimate shows, in particular, that for $N\geqslant \theta n^2$ with $\theta >0$ the $L_p$-norm of a polynomial grows as $n\to\infty$ not faster than the $L_q$-means, $q\geqslant p$, of this polynomial over the nodes of the grid times some power of $n$.

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