(untitled) (Communications in Mathematical Research, 2019)
Based on the theory of variable exponents and BMO norms, we prove the vector-valued inequalities for commutators of singular integrals on both homogeneous and inhomogeneous Herz spaces where the two main indices are variable exponents. Furthermore, we show that a wide class of commutators generated by BMO functions and sublinear operators satisfy vector-valued inequalities.