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proof of Clarkson inequality

Type of Math Object: 
Proof
Major Section: 
Reference

Mathematics Subject Classification

28A25 no label found

Comments

Hello,
in my opinion this proof is not correct. I think you are not allowed to use
|a+b|^p <= |a|^p+|b|^p.
Counter-example:
a,b=1 p = 2
=> |1 + 1|^2=4 is NOT smaller then 1^2+1^2=2.
Iam very interested in an alternative proof.

greets flowwsen

I agree, the proof is wrong.

For a correct proof see e.g. Adams, Fournier "Sobolev Spaces" (in the 2nd edition it's 2.38 in the section on Uniform Convexity of L^p spaces).

darthporter

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