Previous |  Up |  Next


Title: Higher order Riesz transforms for the Dunkl Ornstein-Uhlenbeck operator (English)
Author: Nefzi, Walid
Language: English
Journal: Czechoslovak Mathematical Journal
ISSN: 0011-4642 (print)
ISSN: 1572-9141 (online)
Volume: 69
Issue: 1
Year: 2019
Pages: 257-273
Summary lang: English
Category: math
Summary: 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. (English)
Keyword: Dunkl Laplacian
Keyword: Dunkl Ornstein-Uhlenbeck operator
Keyword: generalized Hermite polynomial
Keyword: Riesz transform
MSC: 26A33
MSC: 42C10
MSC: 42C20
MSC: 43A15
MSC: 47G40
DOI: 10.21136/CMJ.2018.0280-17
Date available: 2019-03-08T15:01:43Z
Last updated: 2019-05-07
Stable URL:
Reference: [1] Chihara, T. S.: Generalized Hermite Polynomials. Thesis (Ph.D.).Purdue University, West Lafayette (1955). MR 2612324
Reference: [2] Dunkl, C. D.: Differential-difference operators associated to reflection groups.Trans. Am. Math. Soc. 311 (1989), 167-183. Zbl 0652.33004, MR 0951883, 10.2307/2001022
Reference: [3] Graczyk, P., Loeb, J. J., López, I., Nowak, A., Urbina, W.: Higher order Riesz transforms, fractional derivatives, and Sobolev spaces for Laguerre expansions.J. Math. Pures Appl. 84 (2005), 375-405. Zbl 1129.42015, MR 2121578, 10.1016/j.matpur.2004.09.003
Reference: [4] Lebedev, N. N.: Special Functions and Their Applications.Dover Publications, New York (1972). Zbl 0271.33001, MR 0350075
Reference: [5] Muckenhoupt, B.: Conjugate functions for Laguerre expansions.Trans. Am. Math. Soc. 147 (1970), 403-418. Zbl 0192.46202, MR 0252945, 10.2307/1995203
Reference: [6] Nefzi, W.: Higher order Riesz transforms for the Dunkl harmonic oscillator.Taiwanese J. Math. 19 (2015), 567-583. Zbl 1357.42006, MR 3332314, 10.11650/tjm.19.2015.4762
Reference: [7] Nowak, A., Roncal, L., Stempak, K.: Riesz transforms for the Dunkl Ornstein-Uhlenbeck operator.Colloq. Math. 118 (2010), 669-684. Zbl 1194.42036, MR 2602173, 10.4064/cm118-2-19
Reference: [8] Nowak, A., Stempak, K.: Riesz transforms for the Dunkl harmonic oscillator.Math. Z. 262 (2009), 539-556. Zbl 1168.44002, MR 2506306, 10.1007/s00209-008-0388-4
Reference: [9] Rosenblum, M.: Generalized Hermite polynomials and the Bose-like oscillator calculus.Nonselfadjoint Operators and Related Topics A. Feintuch et al. Operator Theory: Advances and Applications 73, Birkhäuser, Basel (1994), 369-396. Zbl 0826.33005, MR 1320555
Reference: [10] Rösler, M.: Generalized Hermite polynomials and the heat equation for Dunkl operators.Commun. Math. Phys. 192 (1998), 519-542. Zbl 0908.33005, MR 1620515, 10.1007/s002200050307
Reference: [11] Rösler, M.: Dunkl operators: Theory and applications.E. Koelink et al. Orthogonal Polynomials and Special Functions Lecture Notes in Mathematics 1817, Springer, Berlin (2003), 93-135. Zbl 1029.43001, MR 2022853, 10.1007/3-540-44945-0_3

Fulltext not available (moving wall 24 months)

Partner of
EuDML logo