Estimates for Multilinear Commutators of Generalized Fractional Integral Operators on Weighted Morrey Spaces

Abstract

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 Lb→-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 Iαb→ on weighted Morrey spaces. The main results in this paper are substantial improvements and extensions of some known results.