# L=sup{f''(0)|f in the set ...}

by niklas
Tags: lsupf0|f
 P: 4 Let $$D\subset\mathbb{C}$$ be the unitdisc and $$F=\{f:D\rightarrow D\,|\,\forall z\in D\partial_{\bar{z}}f=0\}$$, calculate $$L=\sup_{f\in F}|f''(0)|$$. Show that there is an $$g\in F$$ with $$g''(0)=L$$. I am a bit stuck. But I think that it might be an idea to start with Cauchy estimate. Any other ideas?