# conjugate index

For $p,q\in \mathbb{R}$, $$ we say $p$ and $q$ are if $\frac{1}{p}+\frac{1}{q}=1$. Formally, we will also define $q=\mathrm{\infty}$ as conjugate to $p=1$ and vice versa.

Conjugate indices are used in the Hölder inequality^{} (http://planetmath.org/HolderInequality) and more generally to define conjugate spaces.

Title | conjugate index |

Canonical name | ConjugateIndex |

Date of creation | 2013-03-22 12:21:35 |

Last modified on | 2013-03-22 12:21:35 |

Owner | CWoo (3771) |

Last modified by | CWoo (3771) |

Numerical id | 9 |

Author | CWoo (3771) |

Entry type | Definition |

Classification | msc 46E30 |

Synonym | conjugate indices |

Synonym | conjugate indexes |

Synonym | conjugate exponent |

Synonym | Holder exponent |

Synonym | Hölder exponent |

Related topic | HolderInequality |

Related topic | BeattysTheorem |

Related topic | BoundedLinearFunctionalsOnLpmu |