 Generalized Holder inequality

ID: generalized-holder-inequality

p_{1}, \dots, p_{n} \in [1, \infty]

satisfy

\sum_{i} 1/ p_{i} = 1

, then

∥ \prod_{i = 1}^{n} f_{i} ∥_{L^{1}} \leq \prod_{i = 1}^{n} ∥ f_{i} ∥_{L^{p_{i}}} .

It follows by induction from the two-factor Holder inequality.

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