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Approaching Bilinear Multipliers via a Functional Calculus
11Mathematical Institute, Universität Bonn, Endenicher Allee 60, 53115 Bonn, Germany.
Abstract:
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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