Conjugate index
# Conjugate index

In mathematics, two real numbers $p,q>1$ are called conjugate indices (or Hölder conjugates) if

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

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

Conjugate indices are used in Hölder's inequality, as well as Young's inequality for products; the latter can be used to prove the former. If $p,q>1$ are conjugate indices, the spaces $L^p$ and $L^q$ are dual to each other (see $L^p$ space).

