Estimates for multilinear commutators of generalized fractional integral operators on weighted morrey spaces

Let l be the infinitesimal generator of an analytic semigroup on l2(rn) with gaussian kernel bounds,and let l-α/2 be the fractional integrals of l for 0 < α < n. assume that b → = (b1,b2,.,bm) is a finite family of locally integrable functions; then the multilinear commutators generated by b → and l-α/2 are defined by lb →-α/2f = [bm,.,[b2,[b1,l -α/2][,.[ f. assume that bj belongs to weighted bmo space,j = 1,2,.,m; the authors obtain the boundedness of l b →-α/2 on weighted morrey spaces. as a special case,when l =-δ is the laplacian operator,the authors also obtain the boundedness of the multilinear fractional commutator i α b → on weighted morrey spaces. the main results in this paper are substantial improvements and extensions of some known results. © 2015 sha he et al.