Fractional integral operators on the mixed $\lambda$-central central Morrey spaces

In this paper, the authors define the mixed $\lambda$-central Morrey spaces and the mixed $\lambda$-central $BMO$ spaces. The boundedness of the fractional integral operators $T_{\alpha }$ and its commutators $[b,T_{\alpha }]$ are established on the mixed $\lambda$-central Morrey spaces, respectively. Furthermore, we also extend these results to the generalized mixed central Morrey spaces.