We prove the Kato–Ponce inequality (fractional normed Leibniz rule) for multiple factors in the setting of multiple weights (\(A_{\vec P}\) weights). This improves existing results to the product of m factors and extends the class of known weights for which the inequality holds.

中文翻译：

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带有 $$A_{\vec P}$$ 权重的加藤-庞塞不等式

我们证明了在多个权重（\(A_{\vec P}\)权重）设置下多个因素的 Kato–Ponce 不等式（分数范数莱布尼茨规则）。这将现有结果改进为m 个因子的乘积，并扩展了不等式成立的已知权重类别。