Big Hankel operators on Hardy spaces of strongly pseudoconvex domains

IF 1.2 4区数学 Q1 MATHEMATICS

Acta Mathematica Scientia Pub Date : 2024-05-01 DOI:10.1007/s10473-024-0301-1

引用次数: 0

Abstract

In this article, we investigate the (big) Hankel operator H_f on the Hardy spaces of bounded strongly pseudoconvex domains Ω in ℂⁿ. We observe that H_f is bounded on H^p (Ω) (1 < p < ∞) if f belongs to BMO and we obtain some characterizations for H_f on H² (Ω) of other pseudoconvex domains. In these arguments, Amar’s L^p-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 H^p(Ω) (1 ≤ p ≤ ∞) of bounded strongly pseudoconvex domains.

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强伪凸域哈代空间上的大汉克尔算子

摘要本文研究ℂn 中有界强伪凸域 Ω 的哈代空间上的（大）汉克尔算子 Hf。我们观察到，如果 f 属于 BMO，则 Hf 在 Hp (Ω) (1 < p < ∞) 上是有界的。在这些论证中，针对 \({{\bar \partial }_b}\) -方程的解，Amar 的 Lp-estimations 和 Berndtsson 的 L2-estimations 起到了至关重要的作用。此外，我们还解决了有界强伪凸域的哈代空间 Hp(Ω) (1 ≤ p ≤ ∞) 的格里森问题。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Acta Mathematica Scientia 数学-数学

CiteScore

2.00

自引率

10.00%

发文量

2614

审稿时长

6 months

期刊介绍： Acta Mathematica Scientia was founded by Prof. Li Guoping (Lee Kwok Ping) in April 1981. The aim of Acta Mathematica Scientia is to present to the specialized readers important new achievements in the areas of mathematical sciences. The journal considers for publication of original research papers in all areas related to the frontier branches of mathematics with other science and technology.