Boundedness of multilinear commutator of fractional integral inmorrey-herz spaces on homogeneous spaces

In this paper, we explore the boundedness property of the multilinear commutator related to the fractional integral operator. By using of the decomposition of function spaces and some general inequalities, especially Minkowski's inequality and Wilde's inequality, we prove the boundedness of this multilinear commutator in Morrey-Herz spaces on homogeneous spaces, namely I-r((b) over bar) is bounded from M(K) over dot(p1,qt)(alpha,lambda) (center dot X) to M(K) over dot(p2,q2)(alpha,lambda) (X).The result established in this paper extends this kind of the fractional integral operator in homogeneous spaces.