Geodesic
Inequalities for trigonometric polynomials in periodic Morrey spaces
Eurasian mathematical journal, Tome 15 (2024) no. 2, pp. 92-100 
V. I. Burenkov; D. J. Joseph. Inequalities for trigonometric polynomials in periodic Morrey spaces. Eurasian mathematical journal, Tome 15 (2024) no. 2, pp. 92-100. http://geodesic.mathdoc.fr/item/EMJ_2024_15_2_a6/
@article{EMJ_2024_15_2_a6,
     author = {V. I. Burenkov and D. J. Joseph},
     title = {Inequalities for trigonometric polynomials in periodic {Morrey} spaces},
     journal = {Eurasian mathematical journal},
     pages = {92--100},
     year = {2024},
     volume = {15},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EMJ_2024_15_2_a6/}
}
TY  - JOUR
AU  - V. I. Burenkov
AU  - D. J. Joseph
TI  - Inequalities for trigonometric polynomials in periodic Morrey spaces
JO  - Eurasian mathematical journal
PY  - 2024
SP  - 92
EP  - 100
VL  - 15
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/EMJ_2024_15_2_a6/
LA  - en
ID  - EMJ_2024_15_2_a6
ER  - 
%0 Journal Article
%A V. I. Burenkov
%A D. J. Joseph
%T Inequalities for trigonometric polynomials in periodic Morrey spaces
%J Eurasian mathematical journal
%D 2024
%P 92-100
%V 15
%N 2
%U http://geodesic.mathdoc.fr/item/EMJ_2024_15_2_a6/
%G en
%F EMJ_2024_15_2_a6

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

A detailed exposition of BernsteinвЂTMs inequality, inequalities of different metrics and of different dimensions for trigonometic polynomials in Lebesgue spaces is given in the book of S.M. Nikol'skii [4]. In this paper, we state analogues of these inequalities in peridoic Morrey spaces.

[1] V. I. Burenkov, Sobolev spaces on domains, Teubner-Texte zur Mathematik, 137, B. G. Teubner Verlagsgesellschaft mbH, Stuttgart, 1997, 312 pp. | MR

[2] V. I. Burenkov, D. J. Joseph, “Inequalities for entire functions of exponential type in Morrey spaces”, Eurasian Math., 13:3 (2022), 92–99 | DOI | MR | Zbl

[3] V. I. Burenkov, D. J. Joseph, “Integral Inequalities for Entire Functions of Exponential Type in Morrey Spaces”, Proc. Math. Steklov Inst., 323 (2023), 81–100 (in Russian) | DOI | MR

[4] V.I. Burenkov, T.V. Tararykova, “An analogue of Young's inequality for convolutions of functions for general Morrey-type spaces”, Tr. MIAN, 293, MAIK, M, 2016, 113–132 (in Russian) | DOI | MR

[5] M. L. Gol'dman, “Description of traces for some function spaces”, Tr. MIAN USSR, 150, 1979, 99–127 (in Russian) | MR | Zbl

[6] I. I. Ibragimov, Extremal properties of entire functions of finite order, Izdat. Akad. Nauk Azerbaijan. SSR, Baku, 1962, 316 pp. (in Russian) | MR

[7] I. I. Ibragimov, “Extremum problems in the class of trigonometric polynomials”, Dokl. Akad. Nauk. SSSR, 121:3 (1958), 415–417 (in Russian) | MR | Zbl

[8] C. B. Morrey, “On the solutions of quasi-linear elliptic partial differential equations”, Trans. Amer. Math. Soc., 43 (1938), 126–166 | DOI | MR | Zbl

[9] S. M. Nikol'skii, Approximation of functions of several variables and embedding theorems, Izd. 2, revised. and additional, Nauka, M., 1977, 456 pp. (in Russian) | MR

[10] V. N. Temlyakov, Multivariate approximation, Cambridge Monogr. Appl. Comput. Math., 32, Cambridge Univer sity Press, Cambridge, 2018, 550 pp. | MR | Zbl