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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     author = {L. V. Sakhno},
     title = {Multivariate $q$-integral $p$-modules and criterion of the generalized differentiability},
     journal = {Izvestiya of Saratov University. Mathematics. Mechanics. Informatics},
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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/