Conjugate index

In mathematics, two real numbers are called conjugate indices (or Hölder conjugates) if

Formally, we also define as conjugate to and .

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 are conjugate indices, the spaces L^p and L^q are dual to each other (see L^p space).

Properties

The following are equivalent characterizations of Hölder conjugates:

See also

• Beatty's theorem

References

• Antonevich, A. Linear Functional Equations, Birkhäuser, 1999. .