Generalized Holder inequality
= Generalized Holder inequality
{c}
{title2=$\sum_i1/p_i=1$}
If $p_1,\ldots,p_n\in[1,\infty]$ satisfy $\sum_i1/p_i=1$, then
$$
\left\|\prod_{i=1}^nf_i\right\|_{L^1}
\leq\prod_{i=1}^n\|f_i\|_{L^{p_i}}.
$$
It follows by induction from the two-factor <Holder inequality>.