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

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

How to cite

top

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

top
  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), 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

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.