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

Abstract

LetLbe the infinitesimal generator of an analytic semigroup onL2(Rn)with Gaussian kernel bounds, and letL-α/2be the fractional integrals ofLfor0<α<n. Assume thatb→=(b1,b2,…,bm)is a finite family of locally integrable functions; then the multilinear commutators generated byb→andL-α/2are defined byLb→-α/2f=[bm,…,[b2,[b1,L-α/2]],…]f. Assume thatbjbelongs to weighted BMO space,j=1,2,…,m; the authors obtain the boundedness ofLb→-α/2on weighted Morrey spaces. As a special case, whenL=-Δis the Laplacian operator, the authors also obtain the boundedness of the multilinear fractional commutatorIαb→on weighted Morrey spaces. The main results in this paper are substantial improvements and extensions of some known results.