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Big Hankel operators on Hardy spaces of strongly pseudoconvex domains

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Abstract

In this article, we investigate the (big) Hankel operator Hf on the Hardy spaces of bounded strongly pseudoconvex domains Ω in ℂn. We observe that Hf is bounded on Hp (Ω) (1 < p < ∞) if f belongs to BMO and we obtain some characterizations for Hf on H2 (Ω) of other pseudoconvex domains. In these arguments, Amar’s Lp-estimations and Berndtsson’s L2-estimations for solutions of the \({{\bar \partial }_b}\)-equation play a crucial role. In addition, we solve Gleason’s problem for Hardy spaces Hp(Ω) (1 ≤ p ≤ ∞) of bounded strongly pseudoconvex domains.

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Authors and Affiliations

  1. School of Mathematical Sciences, Fudan University, Shanghai, 200433, China

    Boyong Chen

  2. Department of Statistics and Mathematics, Shanghai Lixin University of Accounting and Finance, Shanghai, 201209, China

    Liangying Jiang

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  1. Boyong Chen
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  2. Liangying Jiang
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Correspondence to Liangying Jiang.

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Conflict of Interest The authors declare no conflict of interest.

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Chen’s research was supported by the National Natural Science Foundation of China (12271101).

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Chen, B., Jiang, L. Big Hankel operators on Hardy spaces of strongly pseudoconvex domains. Acta Math Sci 44, 789–809 (2024). https://doi.org/10.1007/s10473-024-0301-1

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  • DOI: https://doi.org/10.1007/s10473-024-0301-1

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