Volterra operators between Hardy spaces of vector-valued Dirichlet series
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866913696563855360 |
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| author | Chen, Jiale |
| author_facet | Chen, Jiale |
| contents | Let $2\leq p<\infty$ and $X$ be a complex infinite-dimensional Banach space. It is proved that if $X$ is $p$-uniformly PL-convex, then there is no nontrivial bounded Volterra operator from the weak Hardy space $\mathscr{H}^{\text{weak}}_p(X)$ to the Hardy space $\mathscr{H}^+_p(X)$ of vector-valued Dirichlet series. To obtain this, a Littlewood--Paley inequality for Dirichlet series is established. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_04896 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Volterra operators between Hardy spaces of vector-valued Dirichlet series Chen, Jiale Functional Analysis Let $2\leq p<\infty$ and $X$ be a complex infinite-dimensional Banach space. It is proved that if $X$ is $p$-uniformly PL-convex, then there is no nontrivial bounded Volterra operator from the weak Hardy space $\mathscr{H}^{\text{weak}}_p(X)$ to the Hardy space $\mathscr{H}^+_p(X)$ of vector-valued Dirichlet series. To obtain this, a Littlewood--Paley inequality for Dirichlet series is established. |
| title | Volterra operators between Hardy spaces of vector-valued Dirichlet series |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2404.04896 |