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 Lp and Lq are dual to each other (see Lp space).