The boundedness on Herz-Morrey spaces is established for a class of Marcinkiewicz integral commutators generated by BMO(Rn) function and Marcinkiewicz integrals with rough kernels.

The authors introduce some Herz-Morrey spaces on spaces of homogeneous type, which are the generalizations of the Herz spaces and the classical Morrey spaces.

Boundedness of commutators on Herz-Morrey spaces;

Boundedness of sublinear operators on Herz-Morrey spaces;

Boundedness of multilinear Calderón-Zygmund singular integral operators on Herz-Morrey spaces

Under the inspiration of the definitions of Morrey space and Herz spaces, we have the Morrey-Herz spaces.

Using the relation between homogeneous Morrey-Herz spaces MK·α,λp,q(Rnn) and homogeneous Herz spaces K·α,pq(Rnn),some results on K·α,pq(Rnn) were extended.

In this paper,the authors prove the boundedness of the Caldero\'n-Zygmund operator in the weak Morrey-Herz spaces on homogeneous spaces.

Boundedness of the high order commutators with variable kernels on the homogeneous Morrey-Herz spaces;

Boundedness of fractional multilinear commutators on homogeneous Morrey-Herz spaces;

Some basic inequalities and interpolation theorems on homogeneous Morrey-Herz spaces;