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Russian Mathematics

, Volume 63, Issue 1, pp 42–54 | Cite as

Nikolskii Inequalities for Trigonometric Polynomials in Different Metrics

  • M. K. PotapovEmail author
  • B. V. SimonovEmail author
Article

Abstract

S. M. Nikolsky’s inequalities for trigonometric polynomials in different metrics are well-known. We generalize the inequalities for the sums of trigonometric polynomials.

Key words

Nikolsky inequality metric trigonometric polynomials 

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Notes

Acknowledgments

Supported by Russian Foundation for Basic Research, grant No. 19-01-00457.

References

  1. 1.
    Timan, M. F. The Approximation Theory of Functions of a Real Variable (Fizmatgiz, Moscow, 1960) [in Russian].Google Scholar
  2. 2.
    Hardy, G. G., Littlewood, D. E., Polia, G. The Inequalities (In. lit., Moscow, 1948) [Russian translation].Google Scholar
  3. 3.
    Besov, O.V., Il’in, V. P., Nikolsky, S. M. Integral Representations of Functions and Embedding Theorems (Nauka, Moscow, 1975) [in Russian].Google Scholar
  4. 4.
    Nikolsky, S. M. Approximation of Functions of Many Variables and Embedding Theorems (Nauka, Moscow, 1977) [in Russian].Google Scholar
  5. 5.
    Uninskii, A. P. “Inequalities in the Mixed Norm for Trigonometric Polynomials and Entire Functions of Finite Degree”, Proceedings of All-Union Symposium on Embedding Theorems (Baku, 1966), pp. 212–218 [in Russian].Google Scholar

Copyright information

© Allerton Press, Inc. 2019

Authors and Affiliations

  1. 1.Moscow State UniversityMoscowRussia
  2. 2.Volgograd State Technical UniversityVolgogradRussia

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