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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>.

Generalized Holder inequality

Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 105 / 3 / a / Solution

Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 105 / 3 / b / Solution

Generalized Holder inequality ( $\sum_{i} 1/ p_{i} = 1$ )

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Generalized Holder inequality (∑i​1/pi​=1)

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Generalized Holder inequality ( $\sum_{i} 1/ p_{i} = 1$ )

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