This article is cited in 5 papers

On integral norms for polynomials

R. M. Trigub


Abstract: 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.

UDC: 517.5

MSC: Primary 42A24, 42A28; Secondary 42A08

Received: 10.10.1974

 English version: Mathematics of the USSR-Sbornik, 1976, 30:3, 279–295

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