Riesz transforms for the Dunkl Ornstein–Uhlenbeck operator
Volume 118 / 2010
Colloquium Mathematicum 118 (2010), 669-684
MSC: Primary 42C10, 42C20.
DOI: 10.4064/cm118-2-19
Abstract
We propose a definition of Riesz transforms associated to the Ornstein–Uhlenbeck operator based on the Dunkl Laplacian. In the case related to the group $\mathbb{Z}_2$ it is proved that the Riesz transform is bounded on the corresponding $L^p$ spaces, $1< p< \infty$.
