# proof of Young Inequality

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

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

By exponentiation we obtain the desired result.

Title proof of Young Inequality ProofOfYoungInequality 2013-03-22 13:30:10 2013-03-22 13:30:10 paolini (1187) paolini (1187) 4 paolini (1187) Proof msc 46E30