Boundedness of Commutators for Multilinear Marcinkiewicz Integrals with Generalized Campanato Functions on Generalized Morrey Spaces

This paper is devoted to exploring the mapping properties for the commutator mu O,.b generated by multilinear Marcinkiewicz integral operators mu O with a locally integrable function.b=(b1,center dot center dot center dot, bm) on the generalized Morrey spaces. mu O,.b is bounded from L( p1, f1)(Rn) x center dot center dot center dot xL(pm, fm)(Rn) to L(q, f)(Rn), where L(pi,fi)(Rn), L(q,f)(Rn) are generalized Morrey spaces with certain variable growth condition, that bj(j= 1, center dot center dot center dot, m) is a function in generalized Campanato spaces, which contain the BMO(Rn) and the Lipschitz spaces Lip a( Rn) (0< a= 1) as special examples.