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 Mat. Sb. (N.S.), 1976, Volume 101(143), Number 3(11), Pages 315–333 (Mi msb2902)

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.

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

Bibliographic databases:

UDC: 517.5
MSC: Primary 42A24, 42A28; Secondary 42A08

Citation: R. M. Trigub, “On integral norms for polynomials”, Mat. Sb. (N.S.), 101(143):3(11) (1976), 315–333; Math. USSR-Sb., 30:3 (1976), 279–295

Citation in format AMSBIB
\Bibitem{Tri76} \by R.~M.~Trigub \paper On integral norms for polynomials \jour Mat. Sb. (N.S.) \yr 1976 \vol 101(143) \issue 3(11) \pages 315--333 \mathnet{http://mi.mathnet.ru/msb2902} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=430647} \zmath{https://zbmath.org/?q=an:0339.42010} \transl \jour Math. USSR-Sb. \yr 1976 \vol 30 \issue 3 \pages 279--295 \crossref{https://doi.org/10.1070/SM1976v030n03ABEH002274} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1976FN58700001} 

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Citing articles on Google Scholar: Russian citations, English citations
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This publication is cited in the following articles:
1. N. P. Korneichuk, “S. M. Nikol'skii and the development of research on approximation theory in the USSR”, Russian Math. Surveys, 40:5 (1985), 83–156
2. E.R. Liflyan, “Fourier transforms of radial functions”, Integral Transforms and Special Functions, 4:3 (1996), 279
3. E. R. Liflyand, “Asymptotics of the Fourier Sine Transform of a Function of Bounded Variation”, Math. Notes, 100:1 (2016), 93–99
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