題目：
n 2 n p
(a) Find all extrema of f(x) = Σ x subject to the constraint Σ |x | = 1,
k=1 k k=1 k
where p > 1.
(b) Prove that there exist constants a , b , depending on n, such that for any
n n
real vector x = (x , x ,..., x )
1 2 n
n p 1/p n 2 1/2 n p 1/p
a (Σ |x | ) ≦(Σ x ) ≦b (Σ |x | ) ,
n k=1 k k=1 k n k=1 k
where 1≦p≦2. Find optimal a and b .
n n
比較有問題的是(b)小題，感覺和(a)小題有關，但我不知從何下手。請問要如何解？
謝謝！