混合范数空间中任意复杂度的多参数旗Leibniz定则
Multi-parameter flag Leibniz rules of arbitrary complexity in mixed-norm spaces
摘要：
我们证明了多参数莱布尼茨规则对应的任意复杂性的混合范数空间中的标志paraproducts，包括端点估计。该证明依赖于多线性调和分析技术和Bourgain和Li引入的分解器的定量处理。该论点是强大的，适用于一类通用的乘法器，包括（对称）Mikhlin乘法器的正阶和不对称的变种的部分微分算子和Mikhlin乘法器的正阶。
英文摘要：
We prove multi-parameter Leibniz rules corresponding to flag paraproducts of arbitrary complexity in mixed-norm spaces, including endpoint estimates. The proof relies on multi-linear harmonic analysis techniques and a quantitative treatment of the commutators introduced by Bourgain and Li. The argument is robust and applicable to a generic class of multipliers, including (symmetric) Mikhlin multipliers of positive order and asymmetric variants of partial differential operators and Mikhlin multipliers of positive order.
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