x
Let p > 1，f ≧ 0，f belongs to L^p((0,∞)) and F(x) = ∫ f(t) dt.
0
Show that F(x) = o(x^(1/q)) as x→∞ where (1/p) + (1/q) = 1.
也就是要證明 lim F(x)/x^(1/q) = 0.
x→∞
這題其實是兩小題，另一小題是證明 F(x) = o(x^(1/q)) as x→0.
F(x) = o(x^(1/q)) as x→0 這情況簡單，
那逼近∞時，我試著加一個x的次方進去，再用Holder's inequality
但不行，也試過用Jeanson's inequality，不知是否是函數找的不好，也不行……
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