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SIGMA 5 (2009), 016, 12 pages arXiv:0902.1958
https://doi.org/10.3842/SIGMA.2009.016
Contribution to the Special Issue on Dunkl Operators and Related Topics
Imaginary Powers of the Dunkl Harmonic Oscillator
Adam Nowak and Krzysztof Stempak
Instytut Matematyki i Informatyki, Politechnika Wroclawska,
Wyb. Wyspianskiego 27, 50-370 Wroclaw, Poland
Received October 14, 2008, in final form February 08, 2009; Published online February 11, 2009
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 Z2d. We prove that imaginary powers of this operator are
bounded on Lp, 1 < p < ∞, and from L1 into weak L1.
Key words:
Dunkl operators; Dunkl harmonic oscillator; imaginary powers; Calderón-Zygmund operators.
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