Characterization of weighted Hardy spaces on which all composition operators are bounded - Université d'Artois Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2023

Characterization of weighted Hardy spaces on which all composition operators are bounded

Résumé

We give a complete characterization of the sequences β = (β n) of positive numbers for which all composition operators on H 2 (β) are bounded, where H 2 (β) is the space of analytic functions f on the unit disk D such that ∞ n=0 |a n | 2 β n < +∞ if f (z) = ∞ n=0 a n z n. We prove that all composition operators are bounded on H 2 (β) if and only if β is essentially decreasing and slowly oscillating. We also prove that every automorphism of the unit disk induces a bounded composition operator on H 2 (β) if and only if β is slowly oscillating. We give applications of our results.
Fichier principal
Vignette du fichier
Weighted Hilbert spaces_10-23(2).pdf (454.53 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-04108498 , version 1 (27-05-2023)
hal-04108498 , version 2 (23-10-2023)

Identifiants

  • HAL Id : hal-04108498 , version 2

Citer

Pascal Lefèvre, Daniel Li, Hervé Queffélec, Luis Rodríguez-Piazza. Characterization of weighted Hardy spaces on which all composition operators are bounded. 2023. ⟨hal-04108498v2⟩
29 Consultations
48 Téléchargements

Partager

Gmail Facebook X LinkedIn More