Weak convergence version of sobolev multiplication theorem

Question

Suppose that $1/n-1/p+1/q=0$, and $f_i$ weakly convergent to $f$ in $W^{1,p}$, $g_i$ weakly convergent to $g$ in $W^{1,q}$, can we conclude that $f_i*g_i$ weakly convergent to $f*g$ in $W^{1,p}$?