Exercises
[10J] Having fixed \(s,tβ[1,β]\) with \(s{\lt}t\), show that \(n^{-1/s}\| x\| _ sβ€ n^{-1/t} \| x\| _ t\) (where we agree that \(n^{-1/β}=1\)). (Note that this is an inequality between averages).
(Hint. Set \(πΌ=t/s\) and \(y_ i=|x_ i|^ s\), then use the convexity of \(f(y)=y^{πΌ}\). Another tip: use [10M].)1