Conjugate index

(Redirected from Hölder conjugates)

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.

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