Fractional integral operator for L1 vector fields and its applications

Abstract

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 div-curl inequalities for vector fields.2010 Mathematics Subject Classification. Primary 42B20; Secondary 35F35.