Compactness of Hankel and Toeplitz operators on convex Reinhardt domains in $\mathbb{C}^2$
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908461582778368 |
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| author | Dogan, Nazli Sahutoglu, Sonmez |
| author_facet | Dogan, Nazli Sahutoglu, Sonmez |
| contents | We study compactness of Hankel and Toeplitz operators on Bergman spaces of convex Reinhardt domains in $\mathbb{C}^2$ and we restrict the symbols to the class of functions that are continuous on the closure of the domain. We prove that Toeplitz operators as well as the Hermitian squares of Hankel operators are compact if and only if the Berezin transforms of the operators vanish on the boundary of the domain. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_02339 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Compactness of Hankel and Toeplitz operators on convex Reinhardt domains in $\mathbb{C}^2$ Dogan, Nazli Sahutoglu, Sonmez Complex Variables Functional Analysis 47B35, 32A36 We study compactness of Hankel and Toeplitz operators on Bergman spaces of convex Reinhardt domains in $\mathbb{C}^2$ and we restrict the symbols to the class of functions that are continuous on the closure of the domain. We prove that Toeplitz operators as well as the Hermitian squares of Hankel operators are compact if and only if the Berezin transforms of the operators vanish on the boundary of the domain. |
| title | Compactness of Hankel and Toeplitz operators on convex Reinhardt domains in $\mathbb{C}^2$ |
| topic | Complex Variables Functional Analysis 47B35, 32A36 |
| url | https://arxiv.org/abs/2501.02339 |