Counterexamples for $L^{p}(\mathbb{R})$ spaces inclusion

Question

I know that there's a theorem that gives us inclusions if the space I am considering has a finite measure. However, if I consider the case $L^{1}(\mathbb{R}^n)$ and $L^{2}(\mathbb{R}^n)$, there shouldn't be any inclusion. I know that $L^2$ is not contained in $L^1$, I just have to take $1/x$ as an example. But what is a function that disproves the other inclusion? I can't find any.