Multivariate spectral multipliers for the Dunkl transform and the Dunkl harmonic oscillator

Abstract

In the case G = ℤ 2 d $G=\mathbb {Z}_2^d$ , we prove a multivariate Marcinkiewicz-type multiplier theorem for the Dunkl transform and a multivariate Marcinkiewicz-type multiplier theorem for the system of Dunkl harmonic oscillators.