Geodesic
On integral norms for polynomials
Sbornik. Mathematics, Tome 30 (1976) no. 3, pp. 279-295

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In this paper various transformations of trigonometrical polynomials are introduced; these are then used to deduce asymptotic formulas for the behavior of sequences of integrals of the moduli of the polynomials. As a consequence a definitive form is found for a relationship (in both directions) between the summability and absolute convergence of trigonometric Fourier series which has been noted earlier by the author. Bibliography: 26 titles. 
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R. M. Trigub. On integral norms for polynomials. Sbornik. Mathematics, Tome 30 (1976) no. 3, pp. 279-295. http://geodesic.mathdoc.fr/item/SM_1976_30_3_a0/