Riesz transforms for the Dunkl Ornstein-Uhlenbeck operator

Adam Nowak, Luz Roncal, and Krzysztof Stempak. "Riesz transforms for the Dunkl Ornstein-Uhlenbeck operator." Colloquium Mathematicae 118.2 (2010): 669-684. <http://eudml.org/doc/284210>.

@article{AdamNowak2010,
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 ℤ ₂ it is proved that the Riesz transform is bounded on the corresponding $L^\{p\}$ spaces, 1 < p < ∞.},
author = {Adam Nowak, Luz Roncal, Krzysztof Stempak},
journal = {Colloquium Mathematicae},
keywords = {Dunkl operators; Dunkl Laplacian; Ornstein-Uhlenbeck operator; Riesz transforms; maximal operator; generalized Hermite polynomials},
language = {eng},
number = {2},
pages = {669-684},
title = {Riesz transforms for the Dunkl Ornstein-Uhlenbeck operator},
url = {http://eudml.org/doc/284210},
volume = {118},
year = {2010},
}

TY - JOUR
AU - Adam Nowak
AU - Luz Roncal
AU - Krzysztof Stempak
TI - Riesz transforms for the Dunkl Ornstein-Uhlenbeck operator
JO - Colloquium Mathematicae
PY - 2010
VL - 118
IS - 2
SP - 669
EP - 684
AB - 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 ℤ ₂ it is proved that the Riesz transform is bounded on the corresponding $L^{p}$ spaces, 1 < p < ∞.
LA - eng
KW - Dunkl operators; Dunkl Laplacian; Ornstein-Uhlenbeck operator; Riesz transforms; maximal operator; generalized Hermite polynomials
UR - http://eudml.org/doc/284210
ER -