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Mean Growth of Inner Functions

1973
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Proceedings of the American Mathematical Society
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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