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Статья
2019

Nikolskii Inequalities for Trigonometric Polynomials in Different Metrics


M. K. PotapovM. K. Potapov, B. V. SimonovB. V. Simonov
Русская математика
https://doi.org/10.3103/S1066369X19010055
Abstract / Full Text

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

Author information
  • Moscow State University, GSP-1, Leninskiye Gory, Moscow, 119991, RussiaM. K. Potapov
  • Volgograd State Technical University, pr. Lenina 28, Volgograd, 400005, RussiaB. V. Simonov
References
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  2. Hardy, G. G., Littlewood, D. E., Polia, G. The Inequalities (In. lit., Moscow, 1948) [Russian translation].
  3. Besov, O.V., Il’in, V. P., Nikolsky, S. M. Integral Representations of Functions and Embedding Theorems (Nauka, Moscow, 1975) [in Russian].
  4. Nikolsky, S. M. Approximation of Functions of Many Variables and Embedding Theorems (Nauka, Moscow, 1977) [in Russian].
  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].