Approximation to the Sobolev classes $W_q^r$ of functions of several variables by bilinear forms in $L_p$ for $2\le q\le p\le\infty$

We study the approximation of functions of several variables by bilinear forms that are the pairwise products of functions of fewer variables. The order of approximation of Sobolev classes $W_q^r$ by bilinear forms in $L_p$ for $2 \le q \le p \le\infty$ is found.