Geodesic
Some inequalities for trigonometric polynomials and Fourier coefficients
Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 29, Tome 429 (2014), pp. 64-81 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

The Bernstein inequalities for trigonometric polynomials are generalized. For the sums of Fourier coefficients, upper bounds with certain constants are obtained with respect to values that characterize the structural properties of functions. 
@article{ZNSL_2014_429_a6,
     author = {V. V. Zhuk and G. Yu. Puerov},
     title = {Some inequalities for trigonometric polynomials and {Fourier} coefficients},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {64--81},
     year = {2014},
     volume = {429},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2014_429_a6/}
}
TY  - JOUR
AU  - V. V. Zhuk
AU  - G. Yu. Puerov
TI  - Some inequalities for trigonometric polynomials and Fourier coefficients
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2014
SP  - 64
EP  - 81
VL  - 429
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2014_429_a6/
LA  - ru
ID  - ZNSL_2014_429_a6
ER  - 
%0 Journal Article
%A V. V. Zhuk
%A G. Yu. Puerov
%T Some inequalities for trigonometric polynomials and Fourier coefficients
%J Zapiski Nauchnykh Seminarov POMI
%D 2014
%P 64-81
%V 429
%U http://geodesic.mathdoc.fr/item/ZNSL_2014_429_a6/
%G ru
%F ZNSL_2014_429_a6
V. V. Zhuk; G. Yu. Puerov. Some inequalities for trigonometric polynomials and Fourier coefficients. Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 29, Tome 429 (2014), pp. 64-81. http://geodesic.mathdoc.fr/item/ZNSL_2014_429_a6/

[1] N. K. Bari, Trigonometricheskie ryady, M., 1961 | MR

[2] S. B. Stechkin, “Obobschenie nekotorykh neravenstv S. N. Bernshteina”, Dokl. AN SSSR, 60:9 (1948), 1511–1514 | Zbl

[3] A. A. Konyushkov, “Nailuchshie priblizheniya trigonometricheskimi polinomami i koeffitsienty Fure”, Mat. sb., 44(86):1 (1958), 53–84 | MR | Zbl

[4] A. F. Timan, Teoriya priblizheniya funktsii deistvitelnogo peremennogo, M., 1960

[5] V. V. Zhuk, V. F. Kuzyutin, Approksimatsiya funktsii i chislennoe integrirovanie, SPb., 1995 | MR | Zbl

[6] A. F. Timofeev, Integrirovanie funktsii, M.–L., 1948

[7] G. G. Khardi, Dzh. E. Littlvud, G. Polia, Neravenstva, M., 1948

[8] G. G. Hardy, J. E. Littlewood, “Elementary theorems concerning power series with positive coefficients and moment constants of positive functions”, J. f. Math., 157 (1927), 141–158 | Zbl

[9] V. V. Zhuk, Approksimatsiya periodicheskikh funktsii, L., 1982 | MR | Zbl