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Boundedness of composition operators on general weighted Hardy spaces of analytic functions

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Daniel Li
Hervé Queffélec
  • Function : Author
  • PersonId : 916881
Luis Rodríguez-Piazza
  • Function : Author
  • PersonId : 859619
Pascal Lefèvre

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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Dates and versions

hal-03029931 , version 1 (29-11-2020)
hal-03029931 , version 2 (14-03-2022)

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Daniel Li, Hervé Queffélec, Luis Rodríguez-Piazza, Pascal Lefèvre. Boundedness of composition operators on general weighted Hardy spaces of analytic functions. 2022. ⟨hal-03029931v2⟩
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