$L^{\infty }$-$BMO$ bounds for pseudo-multipliers associated to the harmonic oscillator

Abstract

In this note we investigate some conditions of Hörmander-Mihlin type in order to assure the $L^{\infty }$-$\text{BMO}$ boundedness for pseudo-multipliers of the harmonic oscillator. The ${\text{H}}^1$-$L^1$ continuity for Hermite multipliers also is investigated. The final version of this paper will appear in Rev. Colombiana Mat.

13 pages