Characterization of weighted Hardy spaces on which all composition operators are bounded
| Autor: | Lefèvre, Pascal, Li, Daniel, Queffélec, Hervé, Rodríguez-Piazza, Luis |
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| Rok vydání: | 2023 |
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| Druh dokumentu: | Working Paper |
| Popis: | We give a complete characterization of the sequences $\beta = (\beta_n)$ of positive numbers for which all composition operators on $H^2 (\beta)$ are bounded, where $H^2 (\beta)$ is the space of analytic functions $f$ on the unit disk ${\mathbb D}$ such that $\sum_{n = 0}^\infty |a_n|^2 \beta_n < + \infty$ if $f (z) = \sum_{n = 0}^\infty a_n z^n$. We prove that all composition operators are bounded on $H^2 (\beta)$ if and only if $\beta$ is essentially decreasing and slowly oscillating. We also prove that every automorphism of the unit disk induces a bounded composition operator on $H^2 (\beta)$ if and only if $\beta$ is slowly oscillating. We give applications of our results. Comment: arXiv admin note: substantial text overlap with arXiv:2011.14928 |
| Databáze: | arXiv |
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