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Holder inequality ( $1/ p + 1/ q = 1$ )

For conjugate exponents

p, q

,

\int ∣ f g ∣ \leq ∥ f ∥_{p} ∥ g ∥_{q},

with the analogous inequality

\sum_{n} ∣ x_{n} y_{n} ∣ \leq ∥ x ∥_{p} ∥ y ∥_{q}

for sequences.

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