Some extremal problems on subordinate functions

Let ApAp denote the Bergman space of functions ff analytic in the unit disk DD with ‖f‖Ap={1π∫D|f(z)|pdA(z)}1p<+∞, where p>0p>0, and dA is the Lebesgue area measure. In this paper we investigate some extremal problems on subordinate ApAp functions.