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Properties of functions representable by sine trigonometric series with multiple-monotone coefficients

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Abstract

Functions being sums of sine series with multiple-monotone coefficients are considered. Upper and lower estimates for norms of such functions via their coefficients are presented in the spaces L p (0 < p < ∞).

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References

  1. P. L. Ul’yanov, “Application of the A-Integration to one Class of Trigonometric Series,” Matem. Sborn. 35(3), 469 (1954).

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  2. T. M. Vukolova and M. I. D’yachenko, “Properties of Sums of Trigonometric Series with Monotone Coefficients,” Vestn. Mosk. Univ., Matem. Mekhan. No 3. 22 (1995).

  3. N. K. Bari, Trigonometric Series (GIFML, Moscow, 1961) [in Russian].

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Authors and Affiliations

  1. Faculty of Mechanics and Mathematics, Moscow State University, Leninskie Gory, Moscow, 119991, Russia

    T. M. Vukolova

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  1. T. M. Vukolova
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Additional information

Original Russian Text © T.M. Vukolova, 2007, published in Vestnik Moskovskogo Universiteta, Matematika. Mekhanika, 2007, Vol. 62, No. 6, pp. 61–63.

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Vukolova, T.M. Properties of functions representable by sine trigonometric series with multiple-monotone coefficients. Moscow Univ. Math. Bull. 62, 253–255 (2007). https://doi.org/10.3103/S0027132207060095

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  • DOI: https://doi.org/10.3103/S0027132207060095

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