sto
Posts:
82
Registered:
3/27/08
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| fg | <= 1/2 ( f*f + g*g ) ???
Posted:
Feb 16, 2011 9:28 PM
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Let (X,m) me a measure space and f,g be in L2(X,m)
Presumably it is obvious that for every x in X,
|f(x)g(x)| <= 1/2 ( f(x)*f(x) + g(x)*g(x) )
How do you prove this rigorously? I've tried looking at the RHS as the
area of a rectangle, I've tried the formula for the long side of an
obtuse triangle, I've tried looking at the diagonals of a parallelogram
and nothing works.
Thanks,
-sto
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