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Leibniz-type rules for Coifman-Meyer multiplier operators are studied in thesettings of Triebel-Lizorkin and Besov spaces associated to weights in theMuckenhoupt classes. Even in the unweighted case, improvements on the currentlyknown estimates are obtained. The flexibility of the methods of proofs allowsto prove Leibniz-type rules in a variety of function spaces that includeTriebel-Lizorkin and Besov spaces based on weighted Lebesgue, Lorentz andMorrey spaces as well as variable-exponent Lebesgue spaces. Applications toscattering properties of solutions to certain systems of partial differentialequations involving fractional powers of the Laplacian are presented.

Coifman-Meyer multipliers: Leibniz-type rules and applications to scattering of solutions to PDEs