Conjugate index

In mathematics, two real numbers $p, q>1$ are called conjugate indices if

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

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

Conjugate indices are used in Hölder's inequality. Also, if $p, q>1$ are conjugate indices, the spaces L^p and L^q are dual to each other (see L^p space).

References

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

This article incorporates material from Conjugate index on PlanetMath, which is licensed under the Creative Commons Attribution/Share-Alike License.

This article is issued from Wikipedia - version of the Friday, March 15, 2013. The text is available under the Creative Commons Attribution/Share Alike but additional terms may apply for the media files.

Conjugate index

See also

References