Logarithmic convexity of integral means for analytic functions

Chunjie Wang, Kehe Zhu

We show that the $L^2$ integral mean on $r\D$ of an analytic function in the unit disk $\D$ with respect to the weighted area measure $(1-|z{|}^2{)}^{\alpha }dA(z)$, where $-3\le \alpha \le 0$, is a…