The size of an analytic function as measured by Lévy's time change
The author proves that for a wide class of functions \(\Phi\), f analytic in the unit disk and \(| f'(0)| \geq 1\), it is true that \(E\Phi\) (\(\nu\) (f))\(\geq E(\Phi (\nu (z))\) where \(\nu (f)=\int^{\tau}_{0}| f'(B(s))|^ 2ds\), \(\tau\) being the exit time of the standard, plane, Brownian motion from the unit disk. Also the conjecture P(\(\lambda\leq \nu (f))\geq P(\lambda \leq \nu (z))\) is proved impossible in general.
scientific article; zbMATH DE number 3917408