| 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 |
| idZBL:
|
Zbl 07088783 |
| idMR:
|
MR3923588 |
| DOI:
|
10.21136/CMJ.2018.0280-17 |
| . |
| Date available:
|
2019-03-08T15:01:43Z |
| Last updated:
|
2021-04-05 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/147631 |
| . |
| 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 |
| . |
