Geodesic
Inequalities for differentiable periodic functions and best approximation of one class of functions by another
Izvestiya. Mathematics, Tome 6 (1972) no. 2, pp. 417-428 
N. P. Korneichuk. Inequalities for differentiable periodic functions and best approximation of one class of functions by another. Izvestiya. Mathematics, Tome 6 (1972) no. 2, pp. 417-428. http://geodesic.mathdoc.fr/item/IM2_1972_6_2_a5/
@article{IM2_1972_6_2_a5,
     author = {N. P. Korneichuk},
     title = {Inequalities for differentiable periodic functions and best approximation of one class of functions by another},
     journal = {Izvestiya. Mathematics},
     pages = {417--428},
     year = {1972},
     volume = {6},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1972_6_2_a5/}
}
TY  - JOUR
AU  - N. P. Korneichuk
TI  - Inequalities for differentiable periodic functions and best approximation of one class of functions by another
JO  - Izvestiya. Mathematics
PY  - 1972
SP  - 417
EP  - 428
VL  - 6
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/IM2_1972_6_2_a5/
LA  - en
ID  - IM2_1972_6_2_a5
ER  - 
%0 Journal Article
%A N. P. Korneichuk
%T Inequalities for differentiable periodic functions and best approximation of one class of functions by another
%J Izvestiya. Mathematics
%D 1972
%P 417-428
%V 6
%N 2
%U http://geodesic.mathdoc.fr/item/IM2_1972_6_2_a5/
%G en
%F IM2_1972_6_2_a5

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

New results are obtained in this paper which elucidate properties of differentiable periodic functions connected with rearrangements. These results are applied in order to obtain a sharp estimate of the best uniform approximation of functions of the class $W^rH_\omega$ by functions of the class $W^{r+1}K$.

[1] Korneichuk N. P., “Verkhnie grani nailuchshikh priblizhenii na klassakh differentsiruemykh periodicheskikh funktsii v metrikakh $C$ i $L$”, Dokl. AN SSSR, 190:2 (1970), 269–271

[2] Korneichuk N. P., “Ekstremalnye znacheniya funktsionalov i nailuchshee priblizhenie na klassakh periodicheskikh funktsii”, Izv. AN SSSR. Seriya matem., 35 (1971), 93–124

[3] Stein E. M., “Functions of exponential type”, Ann. Math., 65:3 (1957), 582–592 | DOI | MR | Zbl

[4] Kolmogorov A. N., “O neravenstvakh mezhdu verkhnimi granyami posledovatelnykh proizvodnykh proizvolnoi funktsii na beskonechnom intervale”, Uch. zap. Mosk. un-ta, Matematika, 30:3 (1939), 3–13

[5] Korneichuk N. P., “O nailuchshem ravnomernom priblizhenii na nekotorykh klassakh nepreryvnykh funktsii”, Dokl. AN SSSR, 140:4 (1961), 748–751

[6] Korneichuk N. P., “O nailuchshem ravnomernom priblizhenii differentsiruemye funktsii”, Dokl. AN SSSR, 141:2 (1961), 304–307

[7] Korneichuk N. P., “Tochnoe znachenie nailuchshikh priblizhenii i poperechnikov nekotorykh klassov funktsii”, Dokl. AN SSSR, 150:6 (1963), 1218–1220

[8] Korneichuk N. P., “O nailuchshem priblizhenii nepreryvnykh funktsii”, Izv. AN SSSR. Seriya matem., 27 (1963), 29–44

[9] Ioffe A. D., Tikhomirov V. M., “Dvoistvennost vypuklykh funktsii i ekstremalnye zadachi”, Uspekhi matem. nauk, 23:6(144) (1968), 51–116 | MR | Zbl

[10] Favard J., “Sur l'approximation des fonctions periodiques par des polynomes trigonometriques”, Compt. Rend. Acad. Sci., 203 (1936), 1122–1124 | Zbl

[11] Axiezer N. I., Krein M. G., “O nailuchshem priblizhenii trigonometricheskimi summami differentsiruemykh periodicheskikh funktsii”, Dokl. AN SSSR, 15:3 (1937), 107–112