Compactness of Toeplitz operators with continuous symbols on pseudoconvex domains in $\mathbb{C}^n$
| Autor: | Rodriguez, Tomas Miguel, Sahutoglu, Sonmez |
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| Rok vydání: | 2023 |
| Předmět: | |
| Zdroj: | Proc. Amer. Math. Soc. Ser. B 11 (2024), 406--421 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1090/bproc/217 |
| Popis: | Let $\Omega$ be a bounded pseudoconvex domain in $\mathbb{C}^n$ with Lipschitz boundary and $\phi$ be a continuous function on $\overline{\Omega}$. We show that the Toeplitz operator $T_{\phi}$ with symbol $\phi$ is compact on the weighted Bergman space if and only if $\phi$ vanishes on the boundary of $\Omega$. We also show that compactness of the Toeplitz operator $T^{p,q}_{\phi}$ on $\overline{\partial}$-closed $(p,q)$-forms for $0\leq p\leq n$ and $q\geq 1$ is equivalent to $\phi=0$ on $\Omega$. Comment: Final version. Fixed one reference. To appear in Proc. Amer. Math. Soc |
| Databáze: | arXiv |
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