Stummel functions are uniformly locally $L^2$

Question

In review articles of B. Simon about Schrödinger operators, he mentions that for $n \leq 3$ the condition $$ \lim_{\epsilon \to 0} \sup_x \int_{B(x,\epsilon)} |x-y|^{4-n}|V(y)|^2 dy =0 $$ on a measurable, real-valued function $V$ on $\mathbb R^n$ is equivalent to $$ \sup_x \int_{B(x,1)} |V(y)|^2 dy < \infty. $$ He cites articles by Schechter and by Stummel, but I could not reach them. I was able to prove $\impliedby$ myself -- it is an easy application of Holder's inequality. I would like to ask for some help in proving $\implies$.