Geodesic
Imbedding theorems for classes of functions with mixed norm
Sbornik. Mathematics, Tome 21 (1973) no. 4, pp. 607-618 
Ya. S. Bugrov. Imbedding theorems for classes of functions with mixed norm. Sbornik. Mathematics, Tome 21 (1973) no. 4, pp. 607-618. http://geodesic.mathdoc.fr/item/SM_1973_21_4_a8/
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     author = {Ya. S. Bugrov},
     title = {Imbedding theorems for classes of functions with mixed norm},
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     year = {1973},
     volume = {21},
     number = {4},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1973_21_4_a8/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

We consider spaces$ B_{\vec p,\vec\theta}^{\vec r}(R_n)$ and $W_{\vec p}^{\vec l}(R_n)$ of functions $f(x)$ in the metric of a generalized Lebesgue space $L_{\vec p}(R_n)$, and we prove imbedding theorems for the transition to the metric of $L_{\vec q}(R_n)$. Bibliography: 10 titles.

[1] O. V. Besov, “Issledovanie odnogo semeistva funktsionalnykh prostranstv v svyazi s teoremami vlozheniya i prodolzheniya”, Trudy Matem. in-ta im. V. A. Steklova, LX (1961), 42–81 | MR

[2] O. V. Besov, V. P. Ilin, “Estestvennoe rasshirenie klassa oblastei v teoremakh vlozheniya”, Matem. sb., 75 (117) (1968), 483–495 | MR | Zbl

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

[4] A. Zigmund, Trigonometricheskie ryady, t. I, izd-vo «Mir», Moskva, 1965 | MR

[5] A. Benedek, R. Panzone, “The space $L_p$ with mixed norm”, Duke Math. J., 28:3 (1961), 302–324 | DOI | MR

[6] Ya. S. Bugrov, “Funktsionalnye prostranstva so smeshannoi normoi”, Izv. AN SSSR, seriya matem., 35 (1971), 1137–1158 | MR | Zbl

[7] A. Kh. Gudiev, “Teoremy vlozheniya dlya prostranstv so smeshannoi normoi”, DAN SSSR, 166:3 (1966) | MR | Zbl

[8] V. N. Ilin, “Integralnye predstavleniya funktsii klassov $L_p^l(G)$ i teoremy vlozheniya”, Zapiski nauchn. sem. LOMI, 19 (1970), 95–155

[9] Ya. S. Bugrov, “Teoremy o predstavlenii odnogo klassa funktsii”, Sib. matem. zh., 7:2 (1966), 242–251 | MR | Zbl

[10] O. V. Besov, “Otsenki na oblastyakh modulei gladkosti funktsii i teoremy vlozheniya”, Trudy Matem. in-ta im. V. A. Steklova, CXVIII (1972), 22–46 | MR