Growth properties of Musielak–Orlicz integral means for Riesz potentials

In this paper we are concerned with growth properties of integral means for Riesz potentials of variable order αα of functions in Musielak–Orlicz spaces LΦ(Rn), where ΦΦ is a function of the form Φ(x,t)=tp(x)φ(x,t)Φ(x,t)=tp(x)φ(x,t). Here αα and pp satisfy the log-Hölder condition. We also discuss the size of the exceptional sets using a capacity introduced in Maeda et al. (2011).