Toeplitz operators between large Fock spaces in several complex variables
Let $ \omega $ belong to the weight class $ \mathcal{W} $, the large Fock space $ \mathcal{F}_{\omega}^{p} $ consists of all holomorphic functions $ f $ on $ \mathbb{C}^{n} $ such that the function $ f(\cdot)\omega(\cdot)^{1/2} $ is in $ L^p(\mathbb{C}^{n}, dv) $. In this paper, given a positive Bor...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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AIMS Press
2022-01-01
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| Series: | AIMS Mathematics |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2022076?viewType=HTML |
| Summary: | Let $ \omega $ belong to the weight class $ \mathcal{W} $, the large Fock space $ \mathcal{F}_{\omega}^{p} $ consists of all holomorphic functions $ f $ on $ \mathbb{C}^{n} $ such that the function $ f(\cdot)\omega(\cdot)^{1/2} $ is in $ L^p(\mathbb{C}^{n}, dv) $. In this paper, given a positive Borel measure $ \mu $ on $ {\mathbb C}^n $, we characterize the boundedness and compactness of Toeplitz operator $ T_\mu $ between two large Fock spaces $ F^{p}_\omega $ and $ F^{q}_\omega $ for all possible $ 0 < p, q < \infty $. |
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| ISSN: | 2473-6988 |