AIMS Mathematics (Jan 2022)

Toeplitz operators between large Fock spaces in several complex variables

  • Ermin Wang,
  • Jiajia Xu

DOI
https://doi.org/10.3934/math.2022076
Journal volume & issue
Vol. 7, no. 1
pp. 1293 – 1306

Abstract

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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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