Geodesic
Higher order Riesz transforms for the Dunkl Ornstein-Uhlenbeck operator
Czechoslovak Mathematical Journal, Tome 69 (2019) no. 1, pp. 257-273 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

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.
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.
DOI : 10.21136/CMJ.2018.0280-17
Classification : 26A33, 42C10, 42C20, 43A15, 47G40
Keywords: Dunkl Laplacian; Dunkl Ornstein-Uhlenbeck operator; generalized Hermite polynomial; Riesz transform 
@article{10_21136_CMJ_2018_0280_17,
     author = {Nefzi, Walid},
     title = {Higher order {Riesz} transforms for the {Dunkl} {Ornstein-Uhlenbeck} operator},
     journal = {Czechoslovak Mathematical Journal},
     pages = {257--273},
     year = {2019},
     volume = {69},
     number = {1},
     doi = {10.21136/CMJ.2018.0280-17},
     mrnumber = {3923588},
     zbl = {07088783},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2018.0280-17/}
}
TY  - JOUR
AU  - Nefzi, Walid
TI  - Higher order Riesz transforms for the Dunkl Ornstein-Uhlenbeck operator
JO  - Czechoslovak Mathematical Journal
PY  - 2019
SP  - 257
EP  - 273
VL  - 69
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2018.0280-17/
DO  - 10.21136/CMJ.2018.0280-17
LA  - en
ID  - 10_21136_CMJ_2018_0280_17
ER  - 
%0 Journal Article
%A Nefzi, Walid
%T Higher order Riesz transforms for the Dunkl Ornstein-Uhlenbeck operator
%J Czechoslovak Mathematical Journal
%D 2019
%P 257-273
%V 69
%N 1
%U http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2018.0280-17/
%R 10.21136/CMJ.2018.0280-17
%G en
%F 10_21136_CMJ_2018_0280_17
Nefzi, Walid. Higher order Riesz transforms for the Dunkl Ornstein-Uhlenbeck operator. Czechoslovak Mathematical Journal, Tome 69 (2019) no. 1, pp. 257-273. doi: 10.21136/CMJ.2018.0280-17

[1] Chihara, T. S.: Generalized Hermite Polynomials. Thesis (Ph.D.). Purdue University, West Lafayette (1955). | MR

[2] Dunkl, C. D.: Differential-difference operators associated to reflection groups. Trans. Am. Math. Soc. 311 (1989), 167-183. | DOI | MR | JFM

[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. | DOI | MR | JFM

[4] Lebedev, N. N.: Special Functions and Their Applications. Dover Publications, New York (1972). | MR | JFM

[5] Muckenhoupt, B.: Conjugate functions for Laguerre expansions. Trans. Am. Math. Soc. 147 (1970), 403-418. | DOI | MR | JFM

[6] Nefzi, W.: Higher order Riesz transforms for the Dunkl harmonic oscillator. Taiwanese J. Math. 19 (2015), 567-583. | DOI | MR | JFM

[7] Nowak, A., Roncal, L., Stempak, K.: Riesz transforms for the Dunkl Ornstein-Uhlenbeck operator. Colloq. Math. 118 (2010), 669-684. | DOI | MR | JFM

[8] Nowak, A., Stempak, K.: Riesz transforms for the Dunkl harmonic oscillator. Math. Z. 262 (2009), 539-556. | DOI | MR | JFM

[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. | MR | JFM

[10] Rösler, M.: Generalized Hermite polynomials and the heat equation for Dunkl operators. Commun. Math. Phys. 192 (1998), 519-542. | DOI | MR | JFM

[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. | DOI | MR | JFM

Cité par Sources :