We establish Leibniz-type rules for bilinear and biparameter Fourier multiplier operators with limited Sobolev regularity. Applications of our result are given including the biparameter Leibniz rules, smoothing properties of bilinear-biparameter fractional integrals, and mapping properties of scattering operators for a system of PDEs.

中文翻译：

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双线性和双参数傅立叶乘法器的Leibniz型规则及其应用

我们为Sobolev正则性受限的双线性和双参数傅里叶乘子算子建立了Leibniz型规则。我们的结果的应用包括双参数Leibniz规则，双线性双参数分数积分的平滑特性以及PDE系统的散射算子的映射特性。