Riesz transforms for Dunkl transform

Bechir Amri[1]; Mohamed Sifi[2]

  • [1] Department of Mathematics University of Tunis Preparatory Institute of Engineer Studies of Tunis 1089 Montfleury, Tunis, Tunisia
  • [2] Department of Mathematics University of Tunis El Manar Faculty of Sciences of Tunis 2092 Tunis El Manar, Tunis, Tunisia

Annales mathématiques Blaise Pascal (2012)

  • Volume: 19, Issue: 1, page 247-262
  • ISSN: 1259-1734

Abstract

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In this paper we obtain the L p -boundedness of Riesz transforms for the Dunkl transform for all 1 < p < ∞ .

How to cite

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Amri, Bechir, and Sifi, Mohamed. "Riesz transforms for Dunkl transform." Annales mathématiques Blaise Pascal 19.1 (2012): 247-262. <http://eudml.org/doc/251111>.

@article{Amri2012,
abstract = {In this paper we obtain the $L^p$-boundedness of Riesz transforms for the Dunkl transform for all $1&lt;p&lt;\infty $.},
affiliation = {Department of Mathematics University of Tunis Preparatory Institute of Engineer Studies of Tunis 1089 Montfleury, Tunis, Tunisia; Department of Mathematics University of Tunis El Manar Faculty of Sciences of Tunis 2092 Tunis El Manar, Tunis, Tunisia},
author = {Amri, Bechir, Sifi, Mohamed},
journal = {Annales mathématiques Blaise Pascal},
keywords = {Dunkl transforms; Riesz Transforms; Singular integrals; Riesz transforms; singular integrals},
language = {eng},
month = {1},
number = {1},
pages = {247-262},
publisher = {Annales mathématiques Blaise Pascal},
title = {Riesz transforms for Dunkl transform},
url = {http://eudml.org/doc/251111},
volume = {19},
year = {2012},
}

TY - JOUR
AU - Amri, Bechir
AU - Sifi, Mohamed
TI - Riesz transforms for Dunkl transform
JO - Annales mathématiques Blaise Pascal
DA - 2012/1//
PB - Annales mathématiques Blaise Pascal
VL - 19
IS - 1
SP - 247
EP - 262
AB - In this paper we obtain the $L^p$-boundedness of Riesz transforms for the Dunkl transform for all $1&lt;p&lt;\infty $.
LA - eng
KW - Dunkl transforms; Riesz Transforms; Singular integrals; Riesz transforms; singular integrals
UR - http://eudml.org/doc/251111
ER -

References

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  1. B. Amri, A. Gasmi, M. Sifi, Linear and bilinear multiplier operators for the Dunkl transform, Mediterranean Journal of Mathematics 7 (2010), 503-521 Zbl1209.42006MR2738574
  2. F. Dai, H. Wang, A transference theorem for the Dunkl transform and its applications, Journal of Functional Analysis 258 (2010), 4052-4074 Zbl1246.42015MR2609538
  3. C. F. Dunkl, Differential–Difference operators associated to reflection groups, Trans. Amer. Math. 311 (1989), 167-183 Zbl0652.33004MR951883
  4. S. Hassani, S. Mustapha, M. Sifi, Riesz potentials and fractional maximal function for the Dunkl transform, J. Lie Theory 19 (2009, no. 4), 725-734 Zbl1183.33022MR2599001
  5. M.F.E. de Jeu, The Dunkl transform, Invent. Math. 113 (1993), 147-162 Zbl0789.33007MR1223227
  6. M. Rosler, Dunkl operators: theory and applications, in Orthogonal polynomials and special functions (Leuven, 2002), ℝ N , Lect. Notes Math. 1817 (2003), 93-135 Zbl1029.43001MR2022853
  7. M. Rosler, A positive radial product formula for the Dunkl kernel, Trans. Amer. Math. Soc. 355 (2003), 2413-2438 Zbl1015.33010MR1973996
  8. E. M. Stein, Harmonic Analysis: Reals-Variable Methods, Orthogonality and Oscillatory Integrals, (1993), PrincetonS, New Jersey Zbl0821.42001MR1232192
  9. S. Thangavelu, Y. Xu, Convolution operator and maximal function for Dunkl transform, J. Anal. Math. 97 (2005), 25-55 Zbl1131.43006MR2274972
  10. S. Thangavelu, Y. Xu, Riesz transforms and Riesz potentials for the Dunkl transform, J. Comp. and Appl. Math. 199 (2007), 181-195 Zbl1145.44001MR2267542

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