Approaching bilinear multipliers via a functional calculus

2016/09/05 by Wróbel, Błażej · 1 citation
#26D10 #42B15 #47B38 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1609.01083

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

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• Dunkl paraproducts and fractional Leibniz rules for the Dunkl Laplacian

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