We establish Leibniz type rules for bilinear flag multipliers with limited regularity in the Lebesgue spaces with flag weights. As applications, we obtain flag fractional Leibniz rules with weights, smoothing properties of bilinear flag fractional integrals, and scattering properties for solutions to a certain system of PDEs. Our results appear to be new even in the unweighted case.

中文翻译：

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双线性标志乘法器的加权莱布尼茨型规则

我们在具有标志权重的 Lebesgue 空间中为具有有限规律性的双线性标志乘数建立 Leibniz 类型规则。作为应用，我们获得了带有权重的标志分数莱布尼茨规则、双线性标志分数积分的平滑特性以及特定偏微分方程组解的散射特性。即使在未加权的情况下，我们的结果似乎也是新的。