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Pré-Publication, Document De Travail Année : 2023

On some questions about composition operators on weighted Hardy spaces

Résumé

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.
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Dates et versions

hal-04266590 , version 1 (31-10-2023)

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Pascal Lefèvre, Daniel Li, Hervé Queffélec, Luis Rodríguez-Piazza. On some questions about composition operators on weighted Hardy spaces. 2023. ⟨hal-04266590⟩
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