Higher order Riesz transforms for the Dunkl Ornstein-Uhlenbeck operator

Walid Nefzi

Czechoslovak Mathematical Journal (2019)

  • Volume: 69, Issue: 1, page 257-273
  • ISSN: 0011-4642

Abstract

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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.

How to cite

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Nefzi, Walid. "Higher order Riesz transforms for the Dunkl Ornstein-Uhlenbeck operator." Czechoslovak Mathematical Journal 69.1 (2019): 257-273. <http://eudml.org/doc/294747>.

@article{Nefzi2019,
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.},
author = {Nefzi, Walid},
journal = {Czechoslovak Mathematical Journal},
keywords = {Dunkl Laplacian; Dunkl Ornstein-Uhlenbeck operator; generalized Hermite polynomial; Riesz transform},
language = {eng},
number = {1},
pages = {257-273},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Higher order Riesz transforms for the Dunkl Ornstein-Uhlenbeck operator},
url = {http://eudml.org/doc/294747},
volume = {69},
year = {2019},
}

TY - JOUR
AU - Nefzi, Walid
TI - Higher order Riesz transforms for the Dunkl Ornstein-Uhlenbeck operator
JO - Czechoslovak Mathematical Journal
PY - 2019
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 69
IS - 1
SP - 257
EP - 273
AB - 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.
LA - eng
KW - Dunkl Laplacian; Dunkl Ornstein-Uhlenbeck operator; generalized Hermite polynomial; Riesz transform
UR - http://eudml.org/doc/294747
ER -

References

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  1. Chihara, T. S., Generalized Hermite Polynomials. Thesis (Ph.D.), Purdue University, West Lafayette (1955). (1955) MR2612324
  2. Dunkl, C. D., 10.2307/2001022, Trans. Am. Math. Soc. 311 (1989), 167-183. (1989) Zbl0652.33004MR0951883DOI10.2307/2001022
  3. Graczyk, P., Loeb, J. J., López, I., Nowak, A., Urbina, W., 10.1016/j.matpur.2004.09.003, J. Math. Pures Appl. 84 (2005), 375-405. (2005) Zbl1129.42015MR2121578DOI10.1016/j.matpur.2004.09.003
  4. Lebedev, N. N., Special Functions and Their Applications, Dover Publications, New York (1972). (1972) Zbl0271.33001MR0350075
  5. Muckenhoupt, B., 10.2307/1995203, Trans. Am. Math. Soc. 147 (1970), 403-418. (1970) Zbl0192.46202MR0252945DOI10.2307/1995203
  6. Nefzi, W., 10.11650/tjm.19.2015.4762, Taiwanese J. Math. 19 (2015), 567-583. (2015) Zbl1357.42006MR3332314DOI10.11650/tjm.19.2015.4762
  7. Nowak, A., Roncal, L., Stempak, K., 10.4064/cm118-2-19, Colloq. Math. 118 (2010), 669-684. (2010) Zbl1194.42036MR2602173DOI10.4064/cm118-2-19
  8. Nowak, A., Stempak, K., 10.1007/s00209-008-0388-4, Math. Z. 262 (2009), 539-556. (2009) Zbl1168.44002MR2506306DOI10.1007/s00209-008-0388-4
  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. (1994) Zbl0826.33005MR1320555
  10. Rösler, M., 10.1007/s002200050307, Commun. Math. Phys. 192 (1998), 519-542. (1998) Zbl0908.33005MR1620515DOI10.1007/s002200050307
  11. Rösler, M., 10.1007/3-540-44945-0_3, E. Koelink et al. Orthogonal Polynomials and Special Functions Lecture Notes in Mathematics 1817, Springer, Berlin (2003), 93-135. (2003) Zbl1029.43001MR2022853DOI10.1007/3-540-44945-0_3

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