Abstract
It is proved that ifj is an inner function and ρ(T)=sup|∫(eiγT/j(γ))f(γ)dγ| overf in the unit ball ofH 1, then eitherρ ≡ 1 for allT≧0, or elseρ(T) ↓ 0 exponentially fast asT ↑ ∞. The inner functionsj corresponding to each alternative are classified.
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