Geodesic
On an Inequality of Sidon Type for Trigonometric Polynomials
Matematičeskie zametki, Tome 89 (2011) no. 4, pp. 589-595.

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We establish a lower bound for the uniform norm of the trigonometric polynomial of special form via the sum of the $L^1$-norms of its summands. This result generalizes a theorem due to Kashin and Temlyakov, which, in turn, generalizes the classical Sidon inequality.
Keywords: trigonometric polynomial, Sidon inequality, lacunary sequence, lacunarity index
Mots-clés : Vallée-Poussin kernel. 
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A. O. Radomskii. On an Inequality of Sidon Type for Trigonometric Polynomials. Matematičeskie zametki, Tome 89 (2011) no. 4, pp. 589-595. http://geodesic.mathdoc.fr/item/MZM_2011_89_4_a9/

[1] B. S. Kashin, V. N. Temlyakov, “Ob odnoi norme i approksimatsionnykh kharakteristikakh klassov funktsii mnogikh peremennykh”, Metricheskaya teoriya funktsii i smezhnye voprosy analiza, Sbornik statei. Posvyaschaetsya Petru Lavrentevichu Ulyanovu k ego semidesyatiletiyu, AFTs, M., 1999, 69–99 | MR