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Approaching Bilinear Multipliers via a Functional Calculus.

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

SUBMITTER: Wrobel B

PROVIDER: S-EPMC6294343 | biostudies-other | 2018

REPOSITORIES: biostudies-other

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Approaching Bilinear Multipliers via a Functional Calculus.

Wróbel Błażej B

Journal of geometric analysis 20180130 4

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. ...[more]

PMID: 30595640

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