I'm reading Introduction to PDE of Folland, G. but I'm stuck in the following theorem:
My question is about the $n=2$ case. I tried to do the same argument of $n>2$ but since $N$ and $|\log|x||+1$ are not integrable in zero then I'm not sure how to argue that $\phi\ast N^\varepsilon(0)\to \phi(0)$. For $n>2$, I used that the convergence is uniformly in a set such that zero is in it. Any suggestion would be appreciated.