On some questions about composition operators on weighted Hardy spaces

Lefèvre, Pascal; Li, Daniel; Queffélec, Hervé; Rodríguez-Piazza, Luis

Document type :

Pré-publication ou Document de travail

Title :

On some questions about composition operators on weighted Hardy spaces

Author(s) :

Lefèvre, Pascal [Auteur]
Laboratoire de Mathématiques de Lens [LML]
Université d'Artois [UA]
Li, Daniel [Auteur correspondant]
Laboratoire de Mathématiques de Lens [LML]
Université d'Artois [UA]
Queffélec, Hervé [Auteur]
Université de Lille
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Rodríguez-Piazza, Luis [Auteur]
Universidad de Sevilla = University of Seville

Publication date :

2023-10-31

English keyword(s) :

composition operator
oscillatory integrals
weighted Hardy space

HAL domain(s) :

Mathématiques [math]/Analyse fonctionnelle [math.FA]

English abstract : [en]

We first consider some questions raised by N. Zorboska in her thesis. In particular she asked for which sequences β every symbol φ : D → D with φ ∈ H 2 (β) induces a bounded composition operator C φ on the weighted Hardy ...
Show more >We first consider some questions raised by N. Zorboska in her thesis. In particular she asked for which sequences β every symbol φ : D → D with φ ∈ H 2 (β) induces a bounded composition operator C φ on the weighted Hardy space H 2 (β). We give partial answers and investigate when H 2 (β) is an algebra. We answer negatively to another question in showing that there are a sequence β and φ ∈ H 2 (β) such that ∥φ∥ ∞ < 1 and the composition operator C φ is not bounded on H 2 (β). In a second part, we show that for p ̸ = 2, no automorphism of D, except those that fix 0, induces a bounded composition operator on the Beurling-Sobolev space ℓ p A , and even on the weighted versions of this space.Show less >

Language :

Anglais

Collections :

Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL

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