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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 http://en.wikipedia.org/wiki/H%C3%B6lder's_inequality#Generalization_of_H.C3.B6lder.27s_inequality2012-06-13
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    [A simple proof](http://en.wikipedia.org/wiki/H%C3%B6lder%27s_inequality#Proof_of_H.C3.B6lder.27s_inequality).2012-06-13
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    As did showed you how to do the case $r=1$ for the general case just use the $r=1$ case on $\|f^r g^r\|_1$.2012-06-13

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