You already have the answer, what's the problem with Hölder's inequality?
To put it in easier terms apply the Cauchy-Schwartz inequality to the vectors where you give the usual interior product and norm.
I'm looking a problem that states:
Now if I write them down term by term I would have the following:
which equals to
which is equals to
But how would I show that the above expression is bigger than ?
I tried to use the Holder's inequality by applying the square roof on both side, but then I have:
But I'm still stuck as the p and q are the same in this case.
Any hints? Thank you very much!