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   Author  Topic: Prove Hardy's Theorem  (Read 6629 times)
immanuel78
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Prove Hardy's Theorem  
« on: Dec 5th, 2007, 10:07pm »
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If f is anaytic on B(0;R) and not constant then
 
I(r)=( 1/(2*pi) ) int[ from 0 to 2*pi ] |f( r*exp(i*t) )| dt
 
is strictly increasing and log I(r) is a convex function of log r.
 
 
« Last Edit: Dec 6th, 2007, 2:59am by immanuel78 » IP Logged
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