Compactness of commutators of fractional integral operators on ball Banach function spaces

Let 0<alpha<n and b be a locally integrable function. In this paper, we obtain the characterization of compactness of the iterated commutator (T-Omega,T-alpha)(m)(b) generated by the function b and the fractional integral operator with the homogeneous kernel T-Omega,T-alpha on ball Banach function spaces. As applications, we derive the characterization of compactness via the commutator (T-Omega,T-alpha)(m)(b) on weighted Lebesgue spaces, and further obtain a necessary and sufficient condition for the compactness of the iterated commutator (T-alpha)(m)(b) generated by the function b and the fractional integral operator T-alpha on Morrey spaces. Moreover, we also show the necessary and sufficient condition for the compactness of the commutator [b,T alpha] generated by the function b and the fractional integral operator T alpha on variable Lebesgue spaces and mixed Morrey spaces.