Stein-Weiss inequality in L^{1} norm for vector fields.

In this work, we investigate the limit case p=1 of the classical Stein-Weiss inequality for the Riesz potential. Our main result is a characterization of this inequality for a special class of vector fields associated to cocanceling operators introduced by Van Schaftingen [J. Eur. Math. Soc. (JEMS) 15 (2013), pp. 877–921]. As application, we recover and improve some fractional inequalities associated to vector fields. [ABSTRACT FROM AUTHOR]