Geodesic
Inequality of different metrics for discrete Luxemburg norms in finite-dimensional spaces
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 30 (2024) no. 4, pp. 212-223 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

An exact inequality of different metrics is obtained for discrete Luxemburg norms in a finite-dimensional space. As a consequence, using this inequality, an inequality of different metrics is proved for Luxemburg norms on functions for which there is an upper bound for the norm of a derivative in terms of the norm of the function, and an alternative proof is presented for S.M. Nikol'skii's inequality of different metrics for norms of a trigonometric polynomial in Orlicz spaces.
Keywords: inequality of different metrics, trigonometric polynomial, Orlicz space.
Mots-clés : discrete Luxemburg norm 
@article{TIMM_2024_30_4_a16,
     author = {A. D. P'yankov},
     title = {Inequality of different metrics for discrete {Luxemburg} norms in finite-dimensional spaces},
     journal = {Trudy Instituta matematiki i mehaniki},
     pages = {212--223},
     year = {2024},
     volume = {30},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMM_2024_30_4_a16/}
}
TY  - JOUR
AU  - A. D. P'yankov
TI  - Inequality of different metrics for discrete Luxemburg norms in finite-dimensional spaces
JO  - Trudy Instituta matematiki i mehaniki
PY  - 2024
SP  - 212
EP  - 223
VL  - 30
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/TIMM_2024_30_4_a16/
LA  - ru
ID  - TIMM_2024_30_4_a16
ER  - 
%0 Journal Article
%A A. D. P'yankov
%T Inequality of different metrics for discrete Luxemburg norms in finite-dimensional spaces
%J Trudy Instituta matematiki i mehaniki
%D 2024
%P 212-223
%V 30
%N 4
%U http://geodesic.mathdoc.fr/item/TIMM_2024_30_4_a16/
%G ru
%F TIMM_2024_30_4_a16
A. D. P'yankov. Inequality of different metrics for discrete Luxemburg norms in finite-dimensional spaces. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 30 (2024) no. 4, pp. 212-223. http://geodesic.mathdoc.fr/item/TIMM_2024_30_4_a16/

[1] Nikolskii S.M., “Neravenstva dlya tselykh funktsii konechnoi stepeni i ikh primenenie v teorii differentsiruemykh funktsii mnogikh peremennykh”, Tr. MIAN SSSR, 38 (1951), 244–278 | Zbl

[2] Nikolskii S.M., Priblizhenie funktsii mnogikh peremennykh i teoremy vlozheniya, Izd. 2-e, pererabotannoe i dopolnennoe, Glavnaya redaktsiya fiz.-mat. lit., M., 1977, 456 pp. | MR

[3] Berkolaiko M.Z., Ovchinnikov V.I., “Neravenstva dlya tselykh funktsii eksponentsialnogo tipa v simmetrichnykh prostranstvakh”, Tr. matematicheskogo in-ta AN SSSR, 161 (1983), 3–17 | Zbl

[4] Rodin V.A., “Neravenstva Dzheksona i Nikolskogo dlya trigonometricheskikh polinomov v simmetrichnom prostranstve”, Tr. 7-i zimnei shkoly (Drogobych, 1974), M., 1976, 133–139

[5] Akishev G.A., “O poryadkakh M-chlennykh priblizhenii klassov funktsii simmetrichnogo prostranstva”, Mat. zhurn., 14:4 (54) (2014), 46–71 | Zbl

[6] Marsinkiewisz J., Zygmund A., “Mean values of trigonometrical polynomials”, Fundamental Mathematics, 28 (1937), 9–166

[7] Pyankov A.D., “Neravenstvo raznykh metrik dlya diskretnykh norm Lyuksemburga v konechnomernom prostranstve”, Sovremennye problemy funktsii i ikh prilozheniya, Materialy 22-i Mezhdunar. Saratovskoi zim. shk., posvyaschen. 300-letiyu RAN, sb. statei, Saratov, 2024, 230–233

[8] Krasnoselskii M.A., Rutitskii Ya.B., Vypuklye funktsii i prostranstva Orlicha, Gos. izd-vo fiz.-mat. lit., M., 1958, 271 pp. | MR

[9] Arestov V.V., “Ob integralnykh neravenstvakh dlya trigonometricheskikh polinomov i ikh proizvodnykh”, Mat. izv. Seriya matematicheskaya, 45:1 (1981), 3–22 | MR

[10] Bari N.K., Trigonometricheskie ryady, Gos. izd-vo fiz.-mat. lit., M., 1961, 937 pp.

[11] Pawlewicz A., Wojciechowski M., “Marcinkiewicz sampling theorem for Orlicz spaces”, Positivity, 26:3 (2022), 56 | DOI | MR | Zbl

[12] Milovanovic G.V., Mitrinovic D.S., Rassias Th.M., Topics in polynomials: extremal problems, inequalities, zeros, World Scientific Publishing Co. Ptc. Ltd., Singapore, 1994, 836 pp. | MR | Zbl