  In the spaces $S^p$ of functions of several variables, $2\pi$-periodic in
each variable, we study the approximative properties of operators
$A^\vartriangle_{\varrho,r}$ and $P^\vartriangle_{\varrho,s}$, which generate
two summation methods of multiple Fourier series on triangular regions. In
particular, in the terms of approximation estimates of these operators, we give
a constructive description of classes of functions, whose generalized
derivatives belong to the classes $S^pH_\omega$.
