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Conjugate index

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

Formally, we also define as conjugate to 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 are conjugate indices, the spaces Lp and Lq are dual to each other (see Lp space).

See also

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References

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  • Antonevich, A. 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.