Dans cet article, nous étudions la bornitude des transformées de Riesz associées à la transformée de Dunkl sur les espaces , .
In this paper we obtain the -boundedness of Riesz transforms for the Dunkl transform for all .
@article{AMBP_2012__19_1_247_0, author = {Amri, Bechir and Sifi, Mohamed}, title = {Riesz transforms for Dunkl transform}, journal = {Annales math\'ematiques Blaise Pascal}, volume = {19}, year = {2012}, pages = {247-262}, doi = {10.5802/ambp.312}, zbl = {pre06065098}, mrnumber = {2978321}, language = {en}, url = {http://dml.mathdoc.fr/item/AMBP_2012__19_1_247_0} }
Amri, Bechir; Sifi, Mohamed. Riesz transforms for Dunkl transform. Annales mathématiques Blaise Pascal, Tome 19 (2012) pp. 247-262. doi : 10.5802/ambp.312. http://gdmltest.u-ga.fr/item/AMBP_2012__19_1_247_0/
[1] Linear and bilinear multiplier operators for the Dunkl transform, Mediterranean Journal of Mathematics, Tome 7 (2010), pp. 503-521 | Article | MR 2738574 | Zbl 1209.42006
[2] A transference theorem for the Dunkl transform and its applications, Journal of Functional Analysis, Tome 258 (2010), pp. 4052-4074 | Article | MR 2609538 | Zbl 1246.42015
[3] Differential–Difference operators associated to reflection groups, Trans. Amer. Math., Tome 311 (1989), pp. 167-183 | Article | MR 951883 | Zbl 0652.33004
[4] Riesz potentials and fractional maximal function for the Dunkl transform, J. Lie Theory, Tome 19 (2009, no. 4), pp. 725-734 | MR 2599001 | Zbl 1183.33022
[5] The Dunkl transform, Invent. Math., Tome 113 (1993), pp. 147-162 | Article | MR 1223227 | Zbl 0789.33007
[6] Dunkl operators: theory and applications, in Orthogonal polynomials and special functions (Leuven, 2002), , Lect. Notes Math., Tome 1817 (2003), pp. 93-135 | MR 2022853 | Zbl 1029.43001
[7] A positive radial product formula for the Dunkl kernel, Trans. Amer. Math. Soc., Tome 355 (2003), pp. 2413-2438 | Article | MR 1973996 | Zbl 1015.33010
[8] Harmonic Analysis: Reals-Variable Methods, Orthogonality and Oscillatory Integrals, PrincetonS, New Jersey (1993) | MR 1232192 | Zbl 0821.42001
[9] Convolution operator and maximal function for Dunkl transform, J. Anal. Math., Tome 97 (2005), pp. 25-55 | Article | MR 2274972 | Zbl 1131.43006
[10] Riesz transforms and Riesz potentials for the Dunkl transform, J. Comp. and Appl. Math., Tome 199 (2007), pp. 181-195 | Article | MR 2267542