Fractional integral operator for $L^1$ vector fields and its   applications
  This paper studies fractional integral operator for vector fields in weighted $L^1$. Using the estimates on fractional integral operator and Stein-Weiss inequalities, we can give a new proof for a class of Caffarelli-Kohn-Nirenberg inequalities and establish new $\divg$-$\curl$ inequalities for vector fields. 
Zhibing Zhang
math.CA math.AP math.FA