sto
Posts:
82
Registered:
3/27/08


 fg  <= 1/2 ( f*f + g*g ) ???
Posted:
Feb 16, 2011 9:28 PM


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

