On the relative growth of area for subordinate functions (Q1824720)

Let f be analytic in the open unit disk \(\Delta\) and let A(r,f) denote the area of the region on the Riemann surface onto which the disk \(| z| <r\) is mapped by f. Let f be schlicht in \(\Delta\) and let f be subordinate to F in \(\Delta\). The asymptotic behavior of the ratio A(r,f)/A(r,F) is examined in case F is bounded, or F is mapping onto an infinite strip, or a mapping onto a sector with central angle \(\alpha\) \(\pi\).