Boundedness and Compactness for the Iterated Commutators of Bilinear Fractional Maximal Operators on Weighted Morrey Spaces

Let Mα be the bilinear fractional maximal operator. In this paper, we prove that the commutators Mα,bi in the i-th entry (i=1,2) and the bilinear iterated commutators Mα,b→ of Mα are bounded operators from product weighted Morrey spaces Lp1,κp1q1w1p1,w1q1×Lp2,κp2q2w2p2,w2q2 to weighted Morrey spaces Lq,κvw→q, provided that b∈BMO(Rn) and b→=(b1,b2)∈BMO(Rn)×BMO(Rn). Furthermore, by using the techniques of function decompositions and the Fréchet–Kolmogorov theorem on weighted Morrey spaces, the compactness of Mα,bi(i=1,2) and Mα,b→ are also established whenever b∈CMO(Rn) and b→=(b1,b2)∈CMO(Rn)×CMO(Rn), where CMO(Rn) denotes the closure of Cc∞(Rn) in the BMO(Rn) topology.