Kato–Ponce inequality with \(A_{\vec P}\) weights

We prove the Kato-Ponce inequality (fractional normed Leibniz rule) for multiple factors in the setting of multiple weights ( \(A_{\vec P}\) $A_{\overrightarrow{P}}$ weights). This extends the class of known weights for which the inequality holds from the tensor product of Muckenhoupt weights to a strictly larger weight class.