Abstract
The aim of this paper is to extend the study of Riesz transforms associated to Dunkl Ornstein-Uhlenbeck operator considered by A. Nowak, L. Roncal and K. Stempak to higher order.
Similar content being viewed by others
References
T. S. Chihara: Generalized Hermite Polynomials. Thesis (Ph. D.). Purdue University, West Lafayette, 1955.
C. D. Dunkl: Differential-difference operators associated to reflection groups, Trans. Am. Math. Soc. 311 (1989), 167–183.
P. Graczyk, J. J. Loeb, I. López, A. Nowak, W. Urbina: Higher order Riesz transforms, fractional derivatives, and Sobolev spaces for Laguerre expansions, J. Math. Pures Appl. 84 (2005), 375–405.
N. N. Lebedev: Special Functions and Their Applications. Dover Publications, New York, 1972.
B. Muckenhoupt: Conjugate functions for Laguerre expansions, Trans. Am. Math. Soc. 147 (1970), 403–418.
W. Nefzi: Higher order Riesz transforms for the Dunkl harmonic oscillator, Taiwanese J. Math. 19 (2015), 567–583.
A. Nowak, L. Roncal, K. Stempak: Riesz transforms for the Dunkl Ornstein-Uhlenbeck operator, Colloq. Math. 118 (2010), 669–684.
A. Nowak, K. Stempak: Riesz transforms for the Dunkl harmonic oscillator, Math. Z. 262 (2009), 539–556.
M. Rosenblum: Generalized Hermite polynomials and the Bose-like oscillator calculus. Nonselfadjoint Operators and Related Topics (A. Feintuch et al., eds.). Operator Theory: Advances and Applications 73, Birkhäuser, Basel, 1994, pp. 369–396.
M. Rösler: Generalized Hermite polynomials and the heat equation for Dunkl operators, Commun. Math. Phys. 192 (1998), 519–542.
M. Rösler: Dunkl operators: Theory and applications. Orthogonal Polynomials and Special Functions (E. Koelink et al., eds.). Lecture Notes in Mathematics 1817, Springer, Berlin, 2003, pp. 93–135.
Author information
Authors and Affiliations
Corresponding author
Additional information
Dedicated to my Professor Néjib Ben Salem
Rights and permissions
About this article
Cite this article
Nefzi, W. Higher Order Riesz Transforms for the Dunkl Ornstein-Uhlenbeck Operator. Czech Math J 69, 257–273 (2019). https://doi.org/10.21136/CMJ.2018.0280-17
Received:
Published:
Issue Date:
DOI: https://doi.org/10.21136/CMJ.2018.0280-17