Acta mathematica scientia,Series B ›› 2024, Vol. 44 ›› Issue (3): 789-809.doi: 10.1007/s10473-024-0301-1

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BIG HANKEL OPERATORS ON HARDY SPACES OF STRONGLY PSEUDOCONVEX DOMAINS

Boyong Chen1, Liangying Jiang2,*   

  1. 1. School of Mathematical Sciences, Fudan University, Shanghai 200433, China;
    2. Department of Statistics and Mathematics, Shanghai Lixin University of Accounting and Finance, Shanghai 201209, China
  • Received:2022-12-23 Revised:2023-10-21 Online:2024-06-25 Published:2024-05-21
  • Contact: *E-mail: liangying1231@163.com
  • About author:E-mail: boychen@fudan.edu.cn
  • Supported by:
    Chen's research was supported by the National Natural Science Foundation of China (12271101).

Abstract: In this article, we investigate the (big) Hankel operator $H_f$ on the Hardy spaces of bounded strongly pseudoconvex domains $\Omega$ in $\mathbb{C}^n$. We observe that $H_f$ is bounded on $H^p(\Omega)$ ($1< p<\infty$) if $f$ belongs to BMO and we obtain some characterizations for $H_f$ on $H^2(\Omega)$ of other pseudoconvex domains. In these arguments, Amar's $L^p$-estimations and Berndtsson's $L^2$-estimations for solutions of the $\bar{\partial}_b$-equation play a crucial role. In addition, we solve Gleason's problem for Hardy spaces $H^p(\Omega)$ ($1\le p\le\infty$) of bounded strongly pseudoconvex domains.

Key words: Hankel operator, Hardy space, Bergman space, pseudoconvex domain

CLC Number: 

  • 47B35
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