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.

Locations

• arXiv (Cornell University) - View - PDF
• HAL (Le Centre pour la Communication Scientifique Directe) - View - PDF