Fractional Leibniz Rules Associated to Bilinear Hermite Pseudo-Multipliers

Abstract We obtain a fractional Leibniz rule associated to bilinear Hermite pseudo-multipliers in the context of Hermite Besov and Hermite Triebel–Lizorkin spaces. As a byproduct, we show that the classes of bounded functions in these spaces (which include Hermite Sobolev and Hermite Hardy–Sobolev spaces) are algebras under pointwise multiplication. To obtain these results we develop appropriate decompositions for bilinear pseudo-multipliers and molecular estimates for certain families of functions in the Hermite setting.