Geodesic
On embedding $H_p^{\omega_1,\dots,\omega_\nu}$ classes
Sbornik. Mathematics, Tome 55 (1986) no. 2, pp. 351-381 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Necessary and sufficient conditions are obtained for embedding the function classes $H_p^{\omega_1,\dots,\omega_\nu}$, with given majorants of partial $L_p$-moduli of continuity, in the space $L_q([0,1]^\nu)$ ($1\leqslant p). In particular, for Lipschitz classes $H_p^{\delta^{\alpha_1},\dots,\delta^{\alpha_\nu}}$ ($0<\alpha_i\leqslant1$) a criterion is obtained for embedding in $L_q$ with limit exponent $q=\frac p{1-\overline\alpha p}$, where $\overline\alpha=\bigl(\frac1{\alpha_1}+\dots+\frac1{\alpha_\nu}\bigr)^{-1}$. Bibliography: 13 titles. 
@article{SM_1986_55_2_a3,
     author = {V. I. Kolyada},
     title = {On~embedding $H_p^{\omega_1,\dots,\omega_\nu}$ classes},
     journal = {Sbornik. Mathematics},
     pages = {351--381},
     year = {1986},
     volume = {55},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1986_55_2_a3/}
}
TY  - JOUR
AU  - V. I. Kolyada
TI  - On embedding $H_p^{\omega_1,\dots,\omega_\nu}$ classes
JO  - Sbornik. Mathematics
PY  - 1986
SP  - 351
EP  - 381
VL  - 55
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/SM_1986_55_2_a3/
LA  - en
ID  - SM_1986_55_2_a3
ER  - 
%0 Journal Article
%A V. I. Kolyada
%T On embedding $H_p^{\omega_1,\dots,\omega_\nu}$ classes
%J Sbornik. Mathematics
%D 1986
%P 351-381
%V 55
%N 2
%U http://geodesic.mathdoc.fr/item/SM_1986_55_2_a3/
%G en
%F SM_1986_55_2_a3
V. I. Kolyada. On embedding $H_p^{\omega_1,\dots,\omega_\nu}$ classes. Sbornik. Mathematics, Tome 55 (1986) no. 2, pp. 351-381. http://geodesic.mathdoc.fr/item/SM_1986_55_2_a3/

[1] Ulyanov P. L., “Vlozhenie nekotorykh klassov funktsii $H_p{}^{\omega}$”, Izv. AN SSSR. Ser. matem., 32:3 (1968), 649–686 | Zbl

[2] Golovkin K. K., “Ob odnom obobschenii interpolyatsionnoi teoremy Martsinkevicha”, Tr. MIAN, 102, 1967, 5–28 | MR | Zbl

[3] Besov O. V., Ilin V. P., “Teorema vlozheniya dlya predelnogo pokazatelya”, Matem. zametki, 6:2 (1969), 129–138 | MR | Zbl

[4] Temirgaliev N. T., “Nekotorye teoremy vlozheniya klassov funktsii $H^{\omega}{}_{p,m}$ mnogikh peremennykh”, Izv. AN KazSSR. Ser. fiz.-matem., 5 (1970), 90–92 | MR | Zbl

[5] Pandzhikidze L. K., “Teoremy vlozheniya dlya funktsii mnogikh peremennykh”, Soobsch. AN GruzSSR, 60:1 (1970), 29–31 | MR

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

[7] Osvald P., Moduli nepreryvnosti ravnoizmerimykh funktsii i priblizhenie funktsii algebraicheskimi mnogochlenami v $L_p$, Dis. ... kand. fiz.-matem. nauk, OGU, Odessa, 1978

[8] Besov O. V., Ilin V. P., Nikolskii S. M., Integralnye predstavleniya funktsii i teoremy vlozheniya, Nauka, M., 1975 | MR | Zbl

[9] Nikolskii S. M., Priblizhenie funktsii mnogikh peremennykh i teoremy vlozheniya, Nauka, M., 1977 | MR

[10] Banakh S. S., Kurs funktsIonalnogo analIzu, Radyanska shkola, Kiev, 1948

[11] Oskolkov K. I., “Approksimativnye svoistva summiruemykh funktsii na mnozhestvakh polnoi mery”, Matem. sb., 103(145) (1977), 563–589 | MR | Zbl

[12] Osvald P., “O modulyakh nepreryvnosti ravnoizmerimykh funktsii v klassakh $\varphi(L)$”, Matem. zametki, 17:2 (1975), 231–244 | MR | Zbl

[13] Kolyada V. I., “Teoremy vlozheniya i neravenstva raznykh metrik dlya nailuchshikh priblizhenii”, Matem. sb., 102(144) (1977), 195–215 | Zbl