Conjugate index

In mathematics, two real numbers ${\displaystyle p,q>1}$ are called conjugate indices if

${\displaystyle {\frac {1}{p}}+{\frac {1}{q}}=1.}$

Formally, we will also define ${\displaystyle q=\infty }$ as conjugate to ${\displaystyle p=1}$ and vice versa.

Conjugate indices are used in Hölder's inequality. Also, if ${\displaystyle p,q>1}$ are conjugate indices, the spaces L^p and L^q are dual to each other (see L^p space).