BOUNDEDNESS OF MARCINKIEWICZ INTEGRAL COMMUTATORS WITH VARIABLE KERNEL ON HOMOGENEOUS MORREY-HERZ SPACES

By using the properties of the kernel function Ω(x,2),the boundedness of commutator μ_(Ω,b)(f) is considered,which is generated by a BMO(R~n) function b and the Marcinkiewicz integral operator μ_Ω(f) with variable kernel.It is proved thatμ_(Ω,b) is bounded on the Homogeneous Morrey-Herz spaces MK_(p,q)~(α,λ)(R~n) as Ω(x,z) ∈L~∞(R~n)×L~r(S~(n-1)(r≥1),to generalize the previous non variable kernel results.