Toeplitz operators between large Fock spaces in several complex variables

Ermin Wang; Jiajia Xu; Ermin Wang; Jiajia Xu

doi:10.3934/math.2022076

AIMS Mathematics

2022, Volume 7, Issue 1: 1293-1306. doi: 10.3934/math.2022076

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Research article

Toeplitz operators between large Fock spaces in several complex variables

Ermin Wang ,
Jiajia Xu ^,

School of Mathematics and Statistics, Lingnan Normal University, Guangdong, Zhanjiang 524048, China

Received: 23 July 2021 Accepted: 13 October 2021 Published: 22 October 2021
MSC : 32A25, 47B35

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 $.
- large Fock space,
- boundedness,
- compactness,
- Toeplitz operator
Citation: Ermin Wang, Jiajia Xu. Toeplitz operators between large Fock spaces in several complex variables[J]. AIMS Mathematics, 2022, 7(1): 1293-1306. doi: 10.3934/math.2022076

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Abstract

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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