EDB — 10J

Exercises

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

   Solution 1

   [10K]↺↻