We propose a framework for bilinear multiplier operators defined via the (bivariate) spectral theorem. Under this framework, we prove Coifman–Meyer type multiplier theorems and fractional Leibniz rules. Our theory applies to bilinear multipliers associated with the discrete Laplacian on \(\mathbb {Z}^d,\) general bi-radial bilinear Dunkl multipliers, and to bilinear multipliers associated with the Jacobi expansions.

中文翻译：

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通过函数演算逼近双线性乘法器。

我们提出了一个通过（双变量）谱定理定义的双线性乘法算子的框架。在此框架下，我们证明了Coifman-Meyer型乘法定理和分数莱布尼兹规则。我们的理论适用于与\（\ mathbb {Z} ^ d，\）一般双径向双线性Dunkl乘子上的离散Laplacian相关的双线性乘子，以及与Jacobi展开相关的双线性乘子。