proof of Young Inequality

By the concavity of the $\log$ function we have

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

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