Toeplitz Operators on Fock Space $F_α^{\infty}$
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866912232086962176 |
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| author | Huang, Sui Hu, Xin |
| author_facet | Huang, Sui Hu, Xin |
| contents | In this paper, we study necessary and sufficient conditions for a positive Borel measure $μ$ on the complex space $\mathbb{C}$ to be a $(\infty,q)$ or $(p,\infty)$ (vanishing) Fock-Carleson measure through its Berezin transform. Then we discuss boundedness and compactness of the Toeplitz operator $T_μ$ with a positive Borel measure $μ$ as symbol on Fock space $F_α^{\infty}$. Furthermore, we charaterize these properties of the Toeplitz operator T_φ$ with a symbol $φ$ which is in $BMO$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_09983 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Toeplitz Operators on Fock Space $F_α^{\infty}$ Huang, Sui Hu, Xin Functional Analysis 47B35, 30H20 In this paper, we study necessary and sufficient conditions for a positive Borel measure $μ$ on the complex space $\mathbb{C}$ to be a $(\infty,q)$ or $(p,\infty)$ (vanishing) Fock-Carleson measure through its Berezin transform. Then we discuss boundedness and compactness of the Toeplitz operator $T_μ$ with a positive Borel measure $μ$ as symbol on Fock space $F_α^{\infty}$. Furthermore, we charaterize these properties of the Toeplitz operator T_φ$ with a symbol $φ$ which is in $BMO$. |
| title | Toeplitz Operators on Fock Space $F_α^{\infty}$ |
| topic | Functional Analysis 47B35, 30H20 |
| url | https://arxiv.org/abs/2502.09983 |