# Inequality involving norms.

Suppose $p,q,r \in[1, \infty)$ and ${1\over r} = {1\over p} + {1\over q}$ .

How can I use Minkowski's Inequality for prove below? $$||fg||_r \le ||f||_p||g||_q$$

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It is called Hölder's inequality en.wikipedia.org/wiki/… –  ziyuang Jun 13 '12 at 5:40
–  Did Jun 13 '12 at 7:00
As did showed you how to do the case $r=1$ for the general case just use the $r=1$ case on $\|f^r g^r\|_1$. –  martini Jun 13 '12 at 8:28