Are all the norms of $L^p$ space equivalent?

Are all the norms of $L^p$ space equivalent? That is, for any $p,~q \in R^+$, there exist two positive number $C_1,~C_2$ such that
$$
C_1\|u\|_{L^q} \le \|u\|_{L^p} \le C_2\|u\|_{L^q}.
$$

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