(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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]

2. Relevant equations

The hint is apply the Gauss mean value theorem on [tex]f^2(z)[/tex]

3. 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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# Complex Variables Problem

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