Boundedness of composition operators on general weighted Hardy spaces of analytic functions
Abstract
We characterize the (essentially) decreasing sequences of positive numbers β = (β n) for which all composition operators on H 2 (β) are bounded, where H 2 (β) is the space of analytic functions f in the unit disk such that ∞ n=0 |c n | 2 β n < ∞ if f (z) = ∞ n=0 c n z n. We also give conditions for the boundedness when β is not assumed essentially decreasing.
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