It is true that $L^p(\mathbb{R}^n)\subset \mathscr{S}'(\mathbb{R}^n)$, $1\leq p\leq\infty$?

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Remember that $\mathscr{S}'$ is the space of tempered distributions.

In a certain text they suggest that this statement is true, and that he uses Holder's inequality to prove it. The question is, how do I use it?