Multivariate $q$-integral $p$-modules and criterion of the generalized differentiability

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.