Mean Growth of Inner Functions

Domingo A. Herrero
1973 Proceedings of the American Mathematical Society  
Let A be a closed subset of the closed unit disc. It is shown that there exists a "universal growth function" cp(r, A) such that 1 -ff \q(reix)\2 dxl2tr=0(<p(r, A)) for all inner functions q(z) whose zeroes lie in /ln{|z|<l} and whose singularities in the unit circle lie on /lri{|z|=l}, if and only if the Lebesgue measure of Ar\{\z\ = l} is zero.
doi:10.2307/2038729 fatcat:zot56zfmsneztnu4kgkdp57mze