Schatten class composition operators on the Hardy space of Dirichlet series and a comparison-type principle
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866914787651223552 |
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| author | Bayart, Frédéric Kouroupis, Athanasios |
| author_facet | Bayart, Frédéric Kouroupis, Athanasios |
| contents | We give necessary and sufficient conditions for a composition operator with Dirichlet series symbol to belong to the Schatten classes $S_p$ of the Hardy space $\mathcal{H}^2$ of Dirichlet series. For $p\geq 2$, these conditions lead to a characterization for the subclass of symbols with bounded imaginary parts. Finally, we establish a comparison-type principle for composition operators. Applying our techniques in conjunction with classical geometric function theory methods, we prove the analogue of the polygonal compactness theorem for $\mathcal{H}^2$ and we give examples of bounded composition operators with Dirichlet series symbols on $\mathcal{H}^p,\,p>0$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_05733 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Schatten class composition operators on the Hardy space of Dirichlet series and a comparison-type principle Bayart, Frédéric Kouroupis, Athanasios Functional Analysis Classical Analysis and ODEs Complex Variables We give necessary and sufficient conditions for a composition operator with Dirichlet series symbol to belong to the Schatten classes $S_p$ of the Hardy space $\mathcal{H}^2$ of Dirichlet series. For $p\geq 2$, these conditions lead to a characterization for the subclass of symbols with bounded imaginary parts. Finally, we establish a comparison-type principle for composition operators. Applying our techniques in conjunction with classical geometric function theory methods, we prove the analogue of the polygonal compactness theorem for $\mathcal{H}^2$ and we give examples of bounded composition operators with Dirichlet series symbols on $\mathcal{H}^p,\,p>0$. |
| title | Schatten class composition operators on the Hardy space of Dirichlet series and a comparison-type principle |
| topic | Functional Analysis Classical Analysis and ODEs Complex Variables |
| url | https://arxiv.org/abs/2306.05733 |