Let $x$ be a vector or $\mathbb{R}^n$ and let $n\_p = \|x\|\_p$ and $n\_q=\|x\|\_q$
denotes the $p$-norm and $q$-norms of $x$. I learn (many years ago and maybe I'm wrong...) that there exists two constants $c$ and $C$ such that whatever $x$, we have $cn\_p \leq n\_q \leq Cn\_p$.

* Is it true ?
* If it's true, how can I compute $c$ and $C$ given $p$ and $q$ ?
* What if $p=2$ and $q=\infty$ ?

Thanks !