Geodesic
On imbedding in classes~$\varphi(L)$
Izvestiya. Mathematics , Tome 9 (1975) no. 2, pp. 395-413.

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

In this paper necessary and sufficient conditions are found for imbeddings of the form $H_p^{\omega_1,\dots,\omega_k}\subset L^p\Phi(L)$. It is proved that in the one-dimensional case the corresponding condition on the modulus of continuity of a monotone function $f\in L^p(0,1)$ is not only sufficient but also necessary for $f\in L^p\Phi(L)$. In connection with this the existence is established of a monotone function in $L^p$ with preassigned order of modulus of continuity. Bibliography: 10 items. 
@article{IM2_1975_9_2_a9,
     author = {V. I. Kolyada},
     title = {On imbedding in classes~$\varphi(L)$},
     journal = {Izvestiya. Mathematics },
     pages = {395--413},
     publisher = {mathdoc},
     volume = {9},
     number = {2},
     year = {1975},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1975_9_2_a9/}
}
TY  - JOUR
AU  - V. I. Kolyada
TI  - On imbedding in classes~$\varphi(L)$
JO  - Izvestiya. Mathematics 
PY  - 1975
SP  - 395
EP  - 413
VL  - 9
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_1975_9_2_a9/
LA  - en
ID  - IM2_1975_9_2_a9
ER  - 
%0 Journal Article
%A V. I. Kolyada
%T On imbedding in classes~$\varphi(L)$
%J Izvestiya. Mathematics 
%D 1975
%P 395-413
%V 9
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_1975_9_2_a9/
%G en
%F IM2_1975_9_2_a9
V. I. Kolyada. On imbedding in classes~$\varphi(L)$. Izvestiya. Mathematics , Tome 9 (1975) no. 2, pp. 395-413. http://geodesic.mathdoc.fr/item/IM2_1975_9_2_a9/

[1] Ulyanov P. L., “Vlozhenie nekotorykh klassov funktsii $H_p^\omega$”, Izv. AN SSSR. Ser. matem., 32 (1968), 649–686

[2] Ulyanov P. L., “Teoremy vlozheniya i sootnosheniya mezhdu nailuchshimi priblizheniyami (modulyami nepreryvnosti) v raznykh metrikakh”, Matem. sb., 81(123):1 (1970), 104–131

[3] Leindler L., “On embedding of classes $H_p^\omega$”, Acta Sci. Math., 31:1,2 (1970), 13–31 | MR | Zbl

[4] Storozhenko E. A., “Neobkhodimye i dostatochnye usloviya dlya vlozheniya nekotorykh klassov funktsii”, Izv. AN SSSR. Ser. matem., 37 (1973), 386–398 | Zbl

[5] Temirgaliev N. T., “Nekotorye teoremy vlozheniya klassov funktsii $H_{p,m}^\omega$ mnogikh peremennykh”, Izv. AN KazSSR, ser. fiz.-mat., 1970, no. 5, 90–92 | MR | Zbl

[6] Pandzhikidze L. K., “Teoremy vlozheniya dlya funktsii mnogikh peremennykh”, Soobsch. AN GruzSSR, 61:2 (1971), 281–284 | Zbl

[7] Kolyada V. I., “O vlozhenii nekotorykh klassov funktsii mnogikh peremennykh”, Sib. matem. zh., XIV:4 (1973), 766–790

[8] Kolyada V. I., “O skorosti skhodimosti ortogonalnykh ryadov”, Ukr. matem. zh., 25:1 (1973), 25–38 | MR | Zbl

[9] Khardi G., Littlvud Dzh., Polia G., Neravenstva, IL, M., 1948

[10] Efimov A. V., “Lineinye metody priblizheniya nepreryvnykh periodicheskikh funktsii”, Matem. sb., 54:1 (1961), 51–90 | MR | Zbl