复中值方法
Complex median method
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中文总结 AI 辅助
本文提出复中值方法，去除了高阶交换子有界性刻画中乘子为实值的限制，并证明矩形乘积BMO对双交换子的必要性。
中文摘要 AI 辅助
本文完成了逐点乘法与一大类奇异积分算子的高阶交换子有界性的刻画，其中相应核满足一定的非退化条件。此前该结果仅在逐点乘子为实值函数时成立。我们通过提出一种新颖的复中值方法，最终去除了这一限制。我们还通过证明矩形乘积BMO对双交换子的必要性，展示了该方法的灵活性。
英文摘要
In this paper, we complete the characterization of the boundedness of higher order commutators of pointwise multiplication and a large class of singular integral operators, when the corresponding kernels satisfy certain non-degenerate conditions. This was known with the restriction that the pointwise multiplier is real-valued. We finally remove this restriction by proposing a novel complex median method. We also showcase the flexibility of this method by proving the necessity of the rectangular product BMO for the bi-commutators.
发表机构
- Center for Applied Mathematics, Tianjin University（天津大学应用数学中心）
- School of Mathematical Sciences, Zhejiang Normal University（浙江师范大学数学科学学院）
机构由 AI 辅助整理，请以论文原文为准。
