Conjugate index

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

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

Formally, we also define ${\displaystyle q=\infty }$ as conjugate to ${\displaystyle p=1}$ 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 ${\displaystyle p,q>1}$ are conjugate indices, the spaces L^p and L^q are dual to each other (see L^p space).

See also

• Beatty's theorem

References

• Antonevich, A. Linear Functional Equations, Birkhäuser, 1999. ISBN 3-7643-2931-9.

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