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

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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 $n$. 
@article{SM_1997_188_12_a6,
     author = {I. I. Sharapudinov},
     title = {Estimating the~$L_p$-norm of an~algebraic polynomial in terms of its values at the~nodes of a~uniform grid},
     journal = {Sbornik. Mathematics},
     pages = {1861--1884},
     publisher = {mathdoc},
     volume = {188},
     number = {12},
     year = {1997},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1997_188_12_a6/}
}
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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/