Compactness of Toeplitz operators with continuous symbols on pseudoconvex domains in $\mathbb{C}^n$
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866917777265131520 |
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| author | Rodriguez, Tomas Miguel Sahutoglu, Sonmez |
| author_facet | Rodriguez, Tomas Miguel Sahutoglu, Sonmez |
| contents | Let $Ω$ be a bounded pseudoconvex domain in $\mathbb{C}^n$ with Lipschitz boundary and $ϕ$ be a continuous function on $\overlineΩ$. We show that the Toeplitz operator $T_ϕ$ with symbol $ϕ$ is compact on the weighted Bergman space if and only if $ϕ$ vanishes on the boundary of $Ω$. We also show that compactness of the Toeplitz operator $T^{p,q}_ϕ$ on $\overline{\partial}$-closed $(p,q)$-forms for $0\leq p\leq n$ and $q\geq 1$ is equivalent to $ϕ=0$ on $Ω$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_05013 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Compactness of Toeplitz operators with continuous symbols on pseudoconvex domains in $\mathbb{C}^n$ Rodriguez, Tomas Miguel Sahutoglu, Sonmez Complex Variables Functional Analysis Let $Ω$ be a bounded pseudoconvex domain in $\mathbb{C}^n$ with Lipschitz boundary and $ϕ$ be a continuous function on $\overlineΩ$. We show that the Toeplitz operator $T_ϕ$ with symbol $ϕ$ is compact on the weighted Bergman space if and only if $ϕ$ vanishes on the boundary of $Ω$. We also show that compactness of the Toeplitz operator $T^{p,q}_ϕ$ on $\overline{\partial}$-closed $(p,q)$-forms for $0\leq p\leq n$ and $q\geq 1$ is equivalent to $ϕ=0$ on $Ω$. |
| title | Compactness of Toeplitz operators with continuous symbols on pseudoconvex domains in $\mathbb{C}^n$ |
| topic | Complex Variables Functional Analysis |
| url | https://arxiv.org/abs/2302.05013 |