Geodesic
Analogs of the Jackson–Nikol'skii inequalities for trigonometric polynomials in spaces with nonsymmetric norm
Matematičeskie zametki, Tome 61 (1997) no. 5, pp. 687-699 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The paper is concerned with the evaluation of $$ \sup_{\substack{t_n\in T_n\\t _n\not\equiv 0}} \frac{\|t_n\|_{q_1,q_2}}{\|t_n\|_{p_1,p_2}}, $$ where $\|\cdot\|_{p_1,p_2}$ is a nonsymmetric norm. The order of this number is obtained. Lower bounds involve new polynomials whose properties are studied in detail. In the case $p_1=p_2$, $q_1=q_2$, the estimate obtained is reduced to the well-known Jackson–Nikol'skii inequality. 
@article{MZM_1997_61_5_a5,
     author = {A. I. Kozko},
     title = {Analogs of the {Jackson{\textendash}Nikol'skii} inequalities for trigonometric polynomials in spaces with nonsymmetric norm},
     journal = {Matemati\v{c}eskie zametki},
     pages = {687--699},
     year = {1997},
     volume = {61},
     number = {5},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1997_61_5_a5/}
}
TY  - JOUR
AU  - A. I. Kozko
TI  - Analogs of the Jackson–Nikol'skii inequalities for trigonometric polynomials in spaces with nonsymmetric norm
JO  - Matematičeskie zametki
PY  - 1997
SP  - 687
EP  - 699
VL  - 61
IS  - 5
UR  - http://geodesic.mathdoc.fr/item/MZM_1997_61_5_a5/
LA  - ru
ID  - MZM_1997_61_5_a5
ER  - 
%0 Journal Article
%A A. I. Kozko
%T Analogs of the Jackson–Nikol'skii inequalities for trigonometric polynomials in spaces with nonsymmetric norm
%J Matematičeskie zametki
%D 1997
%P 687-699
%V 61
%N 5
%U http://geodesic.mathdoc.fr/item/MZM_1997_61_5_a5/
%G ru
%F MZM_1997_61_5_a5
A. I. Kozko. Analogs of the Jackson–Nikol'skii inequalities for trigonometric polynomials in spaces with nonsymmetric norm. Matematičeskie zametki, Tome 61 (1997) no. 5, pp. 687-699. http://geodesic.mathdoc.fr/item/MZM_1997_61_5_a5/

[1] Nikolskii S. M., Priblizhenie funktsii mnogikh peremennykh i teoremy vlozheniya, Nauka, M., 1977

[2] Jackson D., “Certain problem of closest approximation”, Bull. Amer. Math. Soc., 39 (1933), 889–906 | DOI | Zbl

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

[4] Dzyadyk V. K., Vvedenie v teoriyu ravnomernogo priblizheniya funktsii polinomami, Nauka, M., 1977 | Zbl

[5] Timan A. F., Teoriya priblizhenii funktsii deistvitelnogo peremennogo, Fizmatgiz, M., 1960