Example of continuous function whose Newtonian potential is not twice differentiable.

Question

I was reading Gilbarg & Trudinger and in there is a statement that the Newtonian potential of a continuous function need not be twice differentiable.

I would appreciate it if someone could provide me an example that would help me to understand this concept properly.

Edit: The Newtonian potential of $f$ is defined as

$$w(x)=\int_{R^n}\Gamma(x-y)f(y)dy$$

where $\Gamma $ is fundamental solution of Laplacian equation.