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Homework Statement
Let f be analytic in the disk |z| <= 1. Prove that for any 0 < r < 1,
[tex]
|f(0)|^2 <= \frac{1}{\pi r^2} \int \int_{x^2 + y^2 <= r^2} |f(z)|^2 dxdy [/tex]
Homework Equations
The hint is apply the Gauss mean value theorem on [tex]f^2(z)[/tex]
The Attempt at a Solution
Having difficulty starting this one. Any hints?
All I've got is
[tex]
f^2(0) = \frac{1}{2\pi} \int(f^2(z))d\theta [/tex]
By applying the Gauss mean value theorem. Then I'm stuck.
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