# proof of Young Inequality

By the concavity of the $\mathrm{log}$ function we have

$$\mathrm{log}ab=\frac{1}{p}\mathrm{log}{a}^{p}+\frac{1}{q}\mathrm{log}{b}^{q}\le \mathrm{log}(\frac{1}{p}{a}^{p}+\frac{1}{q}{b}^{q}).$$ |

By exponentiation we obtain the desired result.

Title | proof of Young Inequality |
---|---|

Canonical name | ProofOfYoungInequality |

Date of creation | 2013-03-22 13:30:10 |

Last modified on | 2013-03-22 13:30:10 |

Owner | paolini (1187) |

Last modified by | paolini (1187) |

Numerical id | 4 |

Author | paolini (1187) |

Entry type | Proof |

Classification | msc 46E30 |