Boundedness of Commutators of Singular Integral Operators with Variable Kernels on the Herz-Type Hardy Space

Let Tb f(x) = p.v.Rn∫K(x,x-y)(b(x)-b(y))f(y)dy be the singular integral operators with variable kernels.We study the bounded properties of T from the homogeneous Herz-type Hardy Space HK q,bn(1-1/q) + δ,p(Rn) to the homogeneous weak Herz space WK qn(1-1/q) + δ-β,p(Rn),and from the homogeneous Herz-type Hardy space HK αq,,bp(Rn) to the homogeneous Herz space K qα-β,p(Rn) respectively.