Acta mathematica scientia,Series B ›› 2023, Vol. 43 ›› Issue (2): 655-667.doi: 10.1007/s10473-023-0211-7

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REVERSE CARLESON MEASURES ON GENERALIZED FOCK SPACES*

Guangfu Cao, Li He, Yiyuan Zhang   

  1. School of Mathematics and Information Science, Guangzhou University, Guangzhou 510006, China
  • Received:2021-11-23 Revised:2022-02-07 Online:2023-03-25 Published:2023-04-12
  • Contact: †Li HE, E-mail: helichangsha1986@163.com.
  • About author:Guangfu Cao, E-mail: guangfucao@163.com; Yiyuan Zhang, E-mail: yiyuanzhang@e.gzhu.edu.cn
  • Supported by:
    Cao was supported by the NNSF of China (12071155), He was supported by the NNSF of China (11871170), the open project of Key Laboratory, school of Mathematical Sciences, Chongqing Normal University (CSSXKFKTM202002), and Zhang was supported by the Innovation Research for the Postgraduates of Guangzhou University (2020GDJC-D08). We are co-first authos.

Abstract: In this paper, we characterize reverse Carleson measures for a class of generalized Fock spaces $F_{\varphi}^{p}$, with $0<p<\infty$ and with $\varphi$ satisfying $d d^{c} \varphi \simeq \omega_{0}$. As an application of these results, we obtain several equivalent characterizations for invertible Toeplitz operators $T_{\psi}$, induced by positive bounded symbols $\psi$ on $F_{\varphi}^{2}$.

Key words: reverse Carleson measures, invertible Toeplitz operators, generalized Fock spaces

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