We consider multilinear operators $T=T(f_1, f_2, \ldots, f_m)$ of the following form: $T(f_1,f_2,\ldots,f_m)(x) =\int_{0}^{\infty}((\varphi_1)_t*f_1)(x)((\varphi_2)_t*f_2)(x) \cdots((\varphi_m)_t*f_m)(x)\,{dt}/{t} $. It is known that under appropriate conditions on $\varphi_j$, there exists $C>0$ such that $\|T(f_1,f_2,\ldots,f_m)\|_{p} \le C\|f_1\|_{p_1}\|f_2\|_{p_2}\cdots\|f_m\|_{p_m}$ for $1