Hilbert matrix operator acting between conformally invariant spaces
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866913811321061376 |
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| author | Bellavita, Carlo Stylogiannis, Georgios |
| author_facet | Bellavita, Carlo Stylogiannis, Georgios |
| contents | In this article we study the action of the the Hilbert matrix operator $\mathcal H$ from the space of bounded analytic functions into conformally invariant Banach spaces. In particular, we describe the norm of $\mathcal{H}$ from $H^\infty$ into $\text{BMOA}$ and we characterize the positive Borel measures $μ$ such that $\mathcal H$ is bounded from $H^\infty$ into the conformally invariant Dirichlet space $M(\mathcal{D}_μ)$. For particular measures $μ$, we also provide the norm of $\mathcal{H}$ from $H^\infty$ into $M(\mathcal{D}_μ)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_01060 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Hilbert matrix operator acting between conformally invariant spaces Bellavita, Carlo Stylogiannis, Georgios Functional Analysis Complex Variables 30H10, 30H35, 30H99, 47B91 In this article we study the action of the the Hilbert matrix operator $\mathcal H$ from the space of bounded analytic functions into conformally invariant Banach spaces. In particular, we describe the norm of $\mathcal{H}$ from $H^\infty$ into $\text{BMOA}$ and we characterize the positive Borel measures $μ$ such that $\mathcal H$ is bounded from $H^\infty$ into the conformally invariant Dirichlet space $M(\mathcal{D}_μ)$. For particular measures $μ$, we also provide the norm of $\mathcal{H}$ from $H^\infty$ into $M(\mathcal{D}_μ)$. |
| title | Hilbert matrix operator acting between conformally invariant spaces |
| topic | Functional Analysis Complex Variables 30H10, 30H35, 30H99, 47B91 |
| url | https://arxiv.org/abs/2408.01060 |