Geodesic
Multivariate $q$-integral $p$-modules and criterion of the generalized differentiability
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 6 (2006) no. 1, pp. 37-45.

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In the article in terms of $L_q$-norm the performance of anisotropic spaces of S. L. Sobolev in space $L_p$ is given. As by one part of numbers probably inequality $p_i>1$, and on another — $p_i=1$ the analog of the theorem of F. Rissa and Hardy–Littlwood is represented in a combined aspect. More common derivation, regular by Schwarz which only in part of variables is Sobolev's also is considered. 
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L. V. Sakhno. Multivariate $q$-integral $p$-modules and criterion of the generalized differentiability. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 6 (2006) no. 1, pp. 37-45. http://geodesic.mathdoc.fr/item/ISU_2006_6_1_a4/

[1] Natanson I. P., Teoriya funktsii veschestvennoi peremennoi, Gostekhizdat, M., 1957

[2] Hardy G., Littlewood J., “Some properties of fractional integrals”, Math., 34 (1932), 403–409 | DOI | MR

[3] Terekhin A. P., “Priblizhenie funktsii ogranichennoi $p$-variatsii”, Izvestiya vuzov. Ser. Matematika, 1965, no. 2, 171–187 | MR

[4] Brudnyi Yu. A., “Kriterii suschestvovaniya proizvodnykh v $L_p$”, Matematicheskii sbornik, 73:1 (1967), 42–64 | MR | Zbl

[5] Terekhin A. P., “Funktsii ogranichennoi $q$-integralnoi $p$-variatsii i teoremy vlozheniya”, Matematicheskii sbornik, 88:2 (1972), 42–64

[6] Terekhin A. P., “Mnogomernaya $q$-integralnaya $p$-variatsiya i obobschennaya po Sobolevu differentsiruemost v $L_p$ funktsii iz $L_p$”, Sibirskii matematicheskii zhurn., 13:6 (1972), 1358–1373 | MR | Zbl

[7] Terekhin A. P., “Smeshannaya $q$-integralnaya $p$-variatsiya i smeshannaya differentsiruemost v $L_p$ funktsii iz $L_p$”, Matematicheskie zametki, 25:3 (1982), 151–166

[8] Sakhno L. V., Mnogomernaya $q$-integralnaya $p$-variatsiya i teoremy vlozheniya, Dep. v VINITI 19.03.81. No 1220-81, Saratov, 1981, 20 pp.

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