Young inequality

Let $a,b>0$ and $p,q\in ]0,\mathrm{\infty }[$ with $1/p+1/q=1$. Then

$$ab\le \frac{a^p}{p}+\frac{b^q}{q}.$$

Title	Young inequality
Canonical name	YoungInequality
Date of creation	2013-03-22 13:30:08
Last modified on	2013-03-22 13:30:08
Owner	paolini (1187)
Last modified by	paolini (1187)
Numerical id	6
Author	paolini (1187)
Entry type	Theorem
Classification	msc 46E30
Related topic	YoungsInequality