Imaginary Powers of the Dunkl Harmonic Oscillator

Abstract

In this paper we continue the study of spectral properties of the Dunkl harmonic oscillator in the context of a finite reflection group on Rd isomorphic to Z_2^d. We prove that imaginary powers of this operator are bounded on L^p, 1 < p < ∞, and from L^1 into weak L^1.

Keywords

• Dunkl operators
• Dunkl harmonic oscillator
• imaginary powers
• Calderón-Zygmund operators