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 general bi-radial bilinear Dunkl multipliers, and to bilinear multipliers associated with the Jacobi expansions.
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