Suppose $f(x)$ is a continuous compactly supported function in $ R^N$ where $N \ge 3$.

Consider the Newtonian potential of $f$ (at least I think this is what it is called)

$$ v(x)=\int_{R^N} \frac{C_N}{|x-y|^{N-2}} f(y) dy$$ where $C_N$ is appropriate positive constant.

My question is that (at least formally) we have $ -\Delta v(x) = f(x)$ in $ R^N$.

My question is there a way to see the equation is satisfied for all $x$.

I know if $ f$ is slightly better than continuous then I think one can do this.

I realize that we can't expect $ v \in C^2$.

thanks
Craig