Hermite Multipliers on Modulation Spaces

2017/12/09 by Bhimani, Divyang G., Balhara, Rakesh, Thangavelu, Sundaram
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1712.03364

Abstract

We study multipliers associated to the Hermite operator H=-Δ+ |x|² on modulation spaces M^p,q(\mathbb R^d). We prove that the operator m(H) is bounded on M^p,q(\mathbb R^d) under standard conditions on m, for suitable choice of p and q. As an application, we point out that the solutions to the free wave and Schrödinger equations associated to H with initial data in a modulation space will remain in the same modulation space for all times. We also point out that Riesz transforms associated to H are bounded on some modulation spaces.

Related

• Sharp estimates of the Schrödinger type propagators on modulation spaces
• Fourier Multipliers and Littlewood-Paley For Modulation Spaces
• The Hartree-Fock equations in modulation spaces
• Step multipliers, Fourier step multipliers and multiplications on quasi-Banach modulation spaces
• Convergence of Hermite expansions in modulation spaces