Re: holder inequality proof


Rob Johnson wrote:
In article <1143479000.431103.167250@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
"Fatou" <fatou19@xxxxxxxxxxxxx> wrote:
just working on the proof of the holder inequality..and a part of the
proof has left me feeling unsure..
f, g, f^2, g^2 elements of L^1

i want to show f.g is integrable
in the proof
|f.g| < or = 1/2 (f^2 +g^2) integrable
im not exactly sure why the last line holds.

i was thinking

(f+g)^2= f^2 +g^2 +2fg
divide it by 2
1/2*(f^2 +g^2) +fg
put a mod around fg, =>
1/2*(f^2 +g^2) + |fg| > or = 0 (all the components inside are all non
negative)
but then i get when taking the |fg| to the other side, a negative on
it, im wondering what i should do..

Consider ( |f| - |g| )^2.

LOL! -sorry! knew it was something small!
thank you


Rob Johnson <rob@xxxxxxxxxxxxxx>
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