Boundedness properties of Hermite pseudo-multipliers

Abstract: Fourier multipliers and pseudo-differential operators are defined by means of the Fourier transform and play an important role in the study of partial differential equations. In the same spirit, Hermite pseudo-multipliers are associated to Hermite expansions and they represent the counterparts to pseudo-differential operators in the Hermite setting. After some preliminaries, we will present results on boundedness properties of pseudo-multipliers in function spaces associated to the Hermite operator. The main tools in the proofs involve new molecular decompositions and molecular synthesis estimates for Hermite Besov and Hermite Triebel-Lizorkin spaces, which allow to obtain boundedness results on spaces for which the smoothness allowed includes non-positive values. In particular, we obtain boundedness results for pseudo-multipliers on Lebesgue and Hermite local Hardy spaces. The talk is based on joint work with Fu Ken Ly (The University of Sydney).

mathematical physicsanalysis of PDEsclassical analysis and ODEscomplex variablesfunctional analysisspectral theory

Audience: researchers in the topic

Harmonic Analysis, Approximation Theory and related topics

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