Commutator Theorems for 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. For any locally integrable function b, the commutators associated with L-α/2 are defined by [b,L-α/2](f)(x)=b(x)L-α/2(f)(x)-L-α/2(bf)(x). When b∈BMO(ω) (weighted BMO space) or b∈BMO, the authors obtain the necessary and sufficient conditions for the boundedness of [b,L-α/2] on weighted Morrey spaces, respectively.