I am trying to prove that
Let $N$ be the Newtonian potential. We observe first that $N$ is a bounded mapping from $L^p(\Omega)$ into itself for $1\le p<\infty$.
Consider the case $p=2$, by approximation, if we have a sequence $(f_n)\subset C^\infty_0(\Omega)$ which converges to $f$ in $L^2(\Omega)$, then $(Nf_n)$ converges to $Nf$ in $W^{2,2}(\Omega)$.
In particular, I cannot explain why the convergence of the 'image' seguence is in $W^{2,2}$.
Thanks a lot