Characterizations of a class of Musielak--Orlicz BMO spaces via commutators of Riesz potential operators

The fractional integral operators $I_α$ can be used to characterize the Musielak--Orlicz Hardy spaces. This paper shows that for $b\in \rm BMO(\mathbb R^n)$, the commutators $[b,I_α]$ generated by fractional integral operators $I_α$ with $b$ are bounded from the Musielak--Orlicz Hardy spaces $H^{φ_1}(\mathbb R^n)$ to the Musielak--Orlicz spaces $L^{φ_2}(\mathbb R^n)$ (where $1