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 $(T_{\mathrm{\Omega },\alpha }{)}_b^m$ generated by the function $b$ and the fractional integral operator with the homogeneous kernel $T_{\mathrm{\Omega },\alpha }$ on ball Banach function spaces. As applications, we derive the characterization of compactness via the commutator $(T_{\mathrm{\Omega },\alpha }{)}_b^m$ on weighted Lebesgue spaces, and further obtain a necessary and sufficient condition for the compactness of the iterated commutator $(T_{\alpha }{)}_b^m$ 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.