Geodesic
Imbedding theorems and relations between best approximations (moduli of continuity) in different metrics
Sbornik. Mathematics, Tome 10 (1970) no. 1, pp. 103-126 
P. L. Ul'yanov. Imbedding theorems and relations between best approximations (moduli of continuity) in different metrics. Sbornik. Mathematics, Tome 10 (1970) no. 1, pp. 103-126. http://geodesic.mathdoc.fr/item/SM_1970_10_1_a7/
@article{SM_1970_10_1_a7,
     author = {P. L. Ul'yanov},
     title = {Imbedding theorems and relations between best approximations (moduli of continuity) in different metrics},
     journal = {Sbornik. Mathematics},
     pages = {103--126},
     year = {1970},
     volume = {10},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1970_10_1_a7/}
}
TY  - JOUR
AU  - P. L. Ul'yanov
TI  - Imbedding theorems and relations between best approximations (moduli of continuity) in different metrics
JO  - Sbornik. Mathematics
PY  - 1970
SP  - 103
EP  - 126
VL  - 10
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/SM_1970_10_1_a7/
LA  - en
ID  - SM_1970_10_1_a7
ER  - 
%0 Journal Article
%A P. L. Ul'yanov
%T Imbedding theorems and relations between best approximations (moduli of continuity) in different metrics
%J Sbornik. Mathematics
%D 1970
%P 103-126
%V 10
%N 1
%U http://geodesic.mathdoc.fr/item/SM_1970_10_1_a7/
%G en
%F SM_1970_10_1_a7

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

In the first part of the work are established imbedding theorems pertaining to arbitrary classes of functions of a single variable $\varphi(L)$, $L\varphi(L)$, $H_p^{\omega(\delta)}$ and $L^\nu\ln^\beta(1+L)$. The second part contains estimates for best approximations (moduli of continuity) in different metrics. It is shown that in certain cases these estimates cannot be strengthened. Bibliography: 14 titles.

[1] G. G. Khardi, D. E. Littlvud, G. Polia, Neravenstva, IL, Moskva, 1948

[2] N. K. Bari, Trigonometricheskie ryady, Fizmatgiz, Moskva, 1961 | MR

[3] A. Zigmund, Trigonometricheskie ryady, Gostekhizdat, Moskva–Leningrad, 1939

[4] A. F. Timan, Teoriya priblizheniya funktsii deistvitelnogo peremennogo, Fizmatgiz, Moskva, 1960

[5] S. B. Stechkin, “O teoreme Kolmogorova–Seliverstova”, Izv. AN SSSR, seriya matem., 17 (1953), 499–512 | Zbl

[6] A. A. Konyushkov, “Nailuchshie priblizheniya trigonometricheskimi polinomami i koeffitsienty Fure”, Matem. sb., 44(86) (1958), 53–84

[7] S. Aljančić, M. Tomić, “Über den Stetigkeitsmodul on Fourier–Reihen mit monotonen Koeffizienten”, Math. Z., 88:3 (1965), 274–284 | DOI | MR | Zbl

[8] P. L. Ulyanov, “O ryadakh po sisteme Khaara”, Matem. sb., 63(105) (1964), 356–391

[9] P. L. Ulyanov, “Ob absolyutnoi i ravnomernoi skhodimosti ryadov Fure”, Matem. sb., 72(114) (1967), 193–225

[10] P. L. Ulyanov, “O vlozhenii nekotorykh klassov funktsii”, Matem. zametki, 1:4 (1967), 405–414

[11] P. L. Ulyanov, “Vlozhenie nekotorykh klassov funktsii”, Izv. AN SSSR, seriya matem., 32 (1968), 649–686

[12] P. L. Ulyanov, “Teoremy vlozheniya i nailuchshie priblizheniya”, DAN SSSR, 184:5 (1969), 1044–1047

[13] S. M. Nikolskii, “Ryad Fure s dannym modulem nepreryvnosti”, DAN SSSR, 52:3 (1946), 191–194

[14] J. H. Hardy, J. E. Littlewood, “A convergence criterion for Fourier-series”, Math. Z., 28:4 (1928), 612–634 | DOI | MR | Zbl