BIG HANKEL OPERATORS ON HARDY SPACES OF STRONGLY PSEUDOCONVEX DOMAINS

doi:10.1007/s10473-024-0301-1

Abstract

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

Boyong Chen, Liangying Jiang. BIG HANKEL OPERATORS ON HARDY SPACES OF STRONGLY PSEUDOCONVEX DOMAINS[J].Acta mathematica scientia,Series B, 2024, 44(3): 789-809.

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