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Mathematical Notes

, Volume 104, Issue 5–6, pp 702–711 | Cite as

Estimates with Sharp Constants of the Sums of Sine Series with Monotone Coefficients of Certain Classes in Terms of the Salem Majorant

  • A. Yu. Popov
  • A. P. Solodov
Article
  • 3 Downloads

Abstract

New estimates of the sums of sine series with monotone coefficients of special classes in terms of the Salem majorant are obtained. The asymptotic sharpness of the obtained estimates for sequences of coefficients from the classes under consideration is proved.

Keywords

sine series asymptotic behavior monotone coefficients 

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References

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    R. Salem, “Determination de l’ordre de grandeur à l’origine de certaines séries trigonométriques,” C. R. Acad. Sci. Paris 186, 1804–1806 (1928).zbMATHGoogle Scholar
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    S. A. Telyakovskii, “On the behavior near the origin of the sine series with convex coefficients,” Publ. Inst. Math. (Beograd) (N. S.) 58 (72), 43–50 (1995).MathSciNetzbMATHGoogle Scholar
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    A. Yu. Popov, “Estimates of the sums of sine series with monotone coefficients of certain classes,” Mat. Zametki 74 (6), 877–888 (2003) [Math. Notes 74 (6), 829–840 (2003)].MathSciNetCrossRefGoogle Scholar
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    A. P. Solodov, “A sharp lower bound for the sum of a sine series with convex coefficients,” Mat. Sb. 207 (12), 124–158 (2016) [Sb.Math. 207 (12), 1743–1777 (2016)].CrossRefzbMATHGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.LomonosovMoscow State UniversityMoscowRussia

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