Generalization of Hardy-Littlewood-Sobolev

Question

My question might be a little ill-posed. I was wondering how the Hardy-Littlewood-Sobolev lemma, i.e. $$\|(-\Delta)^{-\alpha/2}f\|_q \leq \|f\|_p$$ with $1/q = 1/p -\alpha/n$, $1<p<q<\infty$ generalizes if one replaces $(-\Delta)^{-\alpha/2}$ by $(\Delta - g)^{-1}$ (or any power $-\alpha/2$) where $g$ is in some $L^{r}$ for $1\leq r \leq \infty$.