Nikol'skii-Stechkin inequality for trigonometric polynomials in~$L_0$
Matematičeskie zametki, Tome 80 (2006) no. 3, pp. 421-428.

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper, the Nikol'skii–Stechkin inequality for the trigonometric polynomials is generalized to the space $L_0$. The resulting estimates are final.
Keywords: Nikol'skii–Stechkin inequality, trigonometric polynomial
Mots-clés : algebraic polynomial, Euler's formula.
@article{MZM_2006_80_3_a11,
     author = {\`E. A. Storozhenko},
     title = {Nikol'skii-Stechkin inequality for trigonometric polynomials in~$L_0$},
     journal = {Matemati\v{c}eskie zametki},
     pages = {421--428},
     publisher = {mathdoc},
     volume = {80},
     number = {3},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2006_80_3_a11/}
}
TY  - JOUR
AU  - È. A. Storozhenko
TI  - Nikol'skii-Stechkin inequality for trigonometric polynomials in~$L_0$
JO  - Matematičeskie zametki
PY  - 2006
SP  - 421
EP  - 428
VL  - 80
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2006_80_3_a11/
LA  - ru
ID  - MZM_2006_80_3_a11
ER  - 
%0 Journal Article
%A È. A. Storozhenko
%T Nikol'skii-Stechkin inequality for trigonometric polynomials in~$L_0$
%J Matematičeskie zametki
%D 2006
%P 421-428
%V 80
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2006_80_3_a11/
%G ru
%F MZM_2006_80_3_a11
È. A. Storozhenko. Nikol'skii-Stechkin inequality for trigonometric polynomials in~$L_0$. Matematičeskie zametki, Tome 80 (2006) no. 3, pp. 421-428. http://geodesic.mathdoc.fr/item/MZM_2006_80_3_a11/

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

[2] S. M. Nikolskii, “Obobschenie odnogo neravenstva S. N. Bernshteina”, Dokl. AN SSSR, 60:9 (1948), 1507–1510 | MR | Zbl

[3] E. A. Storozhenko, V. G. Krotov, P. Osvald, “Pryamye i obratnye teoremy tipa Dzheksona v prostranstvakh $L_p$, $0

1$”, Matem. sb., 98(140) (1975), 395–415 | MR | Zbl

[4] V. I. Ivanov, “Pryamye i obratnye teoremy teorii priblizhenii v metrike $L_p$ dlya $0

1$”, Matem. zametki, 18:5 (1975), 641–658 | MR | Zbl

[5] P. Osvald, “Nekotorye neravenstva dlya trigonometricheskikh polinomov v metrike $L^p$, $0

1$”, Izv. vuzov. Matem., 1976, no. 7, 65–75 | MR | Zbl

[6] E. A. Storozhenko, Priblizhenie funktsii i teoremy vlozheniya v prostranstvakh $H^p$ i $L^p$, Diss. ... d.f.-m.n., OGU, Odessa, 1978

[7] V. V. Arestov, “Ob integralnykh neravenstvakh dlya trigonometricheskikh polinomov i ikh proizvodnykh”, Izv. AN SSSR. Ser. matem., 45:1 (1981), 3–22 | MR | Zbl

[8] V. V. Arestov, “Integralnye neravenstva dlya algebraicheskikh mnogochlenov na edinichnoi okruzhnosti”, Matem. zametki, 48:4 (1990), 7–18 | MR | Zbl

[9] I. M. Ryzhik, I. S. Gradshtein, Tablitsy integralov, summ, ryadov i proizvedenii, GITTL, M.–L., 1951 | MR | Zbl

[10] E. A. Storozhenko, “K odnoi zadache Malera o nulyakh polinoma i ego proizvodnoi”, Matem. sb., 187:5 (1996), 111–120 | MR | Zbl

[11] E. A. Storozhenko, “Raznostnye neravenstva dlya polinomov v $L_0$”, Matem. studiï, 22:1 (2004), 27–34 | MR | Zbl