Abstract: Using the relation between homogeneous Morrey-Herz spaces MK^α,λ_p,q(Rⁿ) and homogeneous Herz spaces K^α,p_q(Rⁿ), some results on K^α,p_q(Rⁿ) were extended. The CBMO estimates on MK^α,λ_p,q(Rⁿ) were established for the commutator T^b_Ω,l and multilinear operators T^A_Ω,l of fractional integrals with rough kernel. In the meanwhile, the corresponding results for maximal commutators M^b_Ω,l and multilinear maximal operators M^A_Ω,l of fractional integrals were obtained.

Key words: commutator, multilinear operator, fractional integral, rough kernel, MorreyHerz space, central bounded mean oscillation space