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Let [tex]D\subset\mathbb{C}[/tex] be the unitdisc and [tex]F=\{f:D\rightarrow D\,|\,\forall z\in D\partial_{\bar{z}}f=0\}[/tex], calculate [tex]L=\sup_{f\in F}|f''(0)|[/tex]. Show that there is an [tex]g\in F[/tex] with [tex]g''(0)=L[/tex].

I am a bit stuck. But I think that it might be an idea to start with Cauchy estimate. Any other ideas?

I am a bit stuck. But I think that it might be an idea to start with Cauchy estimate. Any other ideas?

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