Bernstein width of a class of functions of finite smoothness

A weak asymptotic formula is obtained for the Bernstein $n$-width in the space $L_q(I^d)$ of the class $F_p^{l,\omega }(I^d)$ of functions on the cube $I^d$ such that their generalized partial derivatives up to order $l$ belong to $L_p(I^d)$ and the moduli of continuity in the space $L_p(I^d)$ of all their derivatives of order $l$ are majorized by a fixed modulus of continuity $\omega$.