Conjugate index

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

: $\backslash frac\{1\}\{p\}\; +\; \backslash frac\{1\}\{q\}\; =\; 1.$

Formally, we also define $q\; =\; \backslash infty$ 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).