Fractional Leibniz rules associated to bilinear Hermite pseudo-multipliers. (English) Zbl 1512.42018

Ly, Fu Ken; Naibo, Virginia

Int. Math. Res. Not. 2023, No. 7, 5401-5437 (2023).

Summary: We obtain a fractional Leibniz rule

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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

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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.

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MSC:

42B15	Multipliers for harmonic analysis in several variables
42B35	Function spaces arising in harmonic analysis
42C15	General harmonic expansions, frames
35S05	Pseudodifferential operators as generalizations of partial differential operators
33C45	Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)
30H25	Besov spaces and \(Q_p\)-spaces

Keywords:

Hermite Besov spaces; Hermite Triebel-Lizorkin spaces