Some extremal problems on subordinate functions

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