- #1

- 173

- 0

Suppose [itex]f \in C^1(0,1)[/itex] and [itex]f(0) = 0[/itex], then

[tex]

f^2(x) \le \int_0^1 f^2(x) dx,

[/tex]

but I was wondering if 1 is the best constant for the inequality. In other words, how do I determine the best bound for

[tex]

f^2(x) \le K \int_0^1 f^2(x) dx,

[/tex]

for K positive?