Multilinear estimates for Calderón commutators
Multilinear estimates for Calderón commutators
复制标题
Calderón 换向器的多线性估计
DOI：
10.1093/imrn/rny197
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发表时间：
2020
影响因子：
1
通讯作者：
Xudong Lai
中科院分区：
文献类型：
--
作者：
Xudong Lai
本文研究了大于2维的高阶（- n）阶Calderón换向子的多线性有界性。我们建立了目标空间的所有多线性端点估计，包括Calderón换向子映射洛伦兹空间的积，这是对第5阶Calderón换向子映射的端点估计的高维非平凡推广。当考虑目标空间时，给出了一些反例，表明这些多线性估计可能不成立。本文的方法似乎具有广泛的应用范围，可以用于建立具有粗糙齐次核的Calderón换向子的类似结果。
In this paper, we investigate the multilinear boundedness properties of the higher (-th) order Calderón commutator for dimensions larger than two. We establish all multilinear endpoint estimates for the target space, including that Calderón commutator maps the product of Lorentz spacesto, which is the higher dimensional nontrivial generalization of the endpoint estimate that the-th order Calderón commutator mapsto. When considering the target spacewith, some counterexamples are given to show that these multilinear estimates may not hold. The method in the present paper seems to have a wide range of applications and it can be applied to establish the similar results for Calderón commutator with a rough homogeneous kernel.