Nikolskii Inequalities for Trigonometric Polynomials in Different Metrics
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 wordsNikolsky inequality metric trigonometric polynomials
Unable to display preview. Download preview PDF.
Supported by Russian Foundation for Basic Research, grant No. 19-01-00457.
- 1.Timan, M. F. The Approximation Theory of Functions of a Real Variable (Fizmatgiz, Moscow, 1960) [in Russian].Google Scholar
- 2.Hardy, G. G., Littlewood, D. E., Polia, G. The Inequalities (In. lit., Moscow, 1948) [Russian translation].Google Scholar
- 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.Nikolsky, S. M. Approximation of Functions of Many Variables and Embedding Theorems (Nauka, Moscow, 1977) [in Russian].Google Scholar
- 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