  In this work, we investigate the limit case $p=1$ of the classical
Stein--Weiss inequality for the Riesz potential.We present a characterization
for a special class of vector fields associated to cocanceling operators
introduced by Van Schaftingen in arXiv:1104.0192. As an application, we recover
some div-curl inequalities found in the literature. In addition, we discuss a
two-weight inequality with general weights in the scalar case, extending the
previous result of Sawyer to this case.
