Holder inequality

$LaTeX: \|x y\|_1 \le \|x\|_p \|y\|_q$,
where $LaTeX: \|\cdot\|_k$ denotes the $LaTeX: L_k$ norm, $LaTeX: p > 1$, and $LaTeX: 1/p + 1/q = 1$. Equality holds if and only if $LaTeX: |x|^p = a|y|^q$ for some scalar $LaTeX: a$. (Note: this is the Cauchy-Schwartz inequality if $LaTeX: p = q = 2$.)