Generalized Hilbert matrix operators acting on Bergman spaces
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arXiv
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| Auteurs principaux: | , , , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866915338501750784 |
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| author | Bellavita, Carlo Daskalogiannis, Vassilis Miihkinen, Santeri Norrbo, David Stylogiannis, Georgios Virtanen, J. A. |
| author_facet | Bellavita, Carlo Daskalogiannis, Vassilis Miihkinen, Santeri Norrbo, David Stylogiannis, Georgios Virtanen, J. A. |
| contents | In this article we study the generalized Hilbert matrix operator $Γ_μ$ acting on the Bergman spaces $A^p$ of the unit disc for $1\leq p<\infty$. In particular, we characterize the measures $μ$ for which the operator $Γ_μ$ is bounded and we provide estimates of its operator norm. Finally, we also describe when $Γ_μ$ is compact by computing its essential norm. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_13569 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Generalized Hilbert matrix operators acting on Bergman spaces Bellavita, Carlo Daskalogiannis, Vassilis Miihkinen, Santeri Norrbo, David Stylogiannis, Georgios Virtanen, J. A. Complex Variables Functional Analysis 30H20, 47B91 In this article we study the generalized Hilbert matrix operator $Γ_μ$ acting on the Bergman spaces $A^p$ of the unit disc for $1\leq p<\infty$. In particular, we characterize the measures $μ$ for which the operator $Γ_μ$ is bounded and we provide estimates of its operator norm. Finally, we also describe when $Γ_μ$ is compact by computing its essential norm. |
| title | Generalized Hilbert matrix operators acting on Bergman spaces |
| topic | Complex Variables Functional Analysis 30H20, 47B91 |
| url | https://arxiv.org/abs/2407.13569 |