On the boundedness of pseudo-differential operators associated with the Dunkl transform on the real line

被引：3

作者：

Amri, Bechir ^{[1
]}

Mustapha, Sami ^{[2
]}

Sifi, Mohamed ^{[3
]}

机构：

[1] Univ Tunis, IPEIT, Dept Math, Montfleury Tunis 1089, Tunisia

[2] Univ Paris VI, Inst Math Jussieu, F-75013 Paris, France

[3] Univ Tunis El Manar, Fac Sci Tunis, Dept Math, Tunis 2092, Tunisia

来源：

ADVANCES IN PURE AND APPLIED MATHEMATICS | 2011年 / 2卷 / 01期

关键词：

Dunkl transform; pseudo-differential operators; singular integrals;

D O I：

10.1515/APAM.2010.028

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we consider pseudo-differential operators associated with the Dunkl transform on the real line. We establish the Calderon-Vaillancourt theorem for such operators. We also obtain the L-p-boundedness for the Hormander's class S-1,delta(0) (0 <= delta < 1).

引用

页码：89 / 107

页数：19

共 13 条

[1] Abdelkefi C., Amri B., Sifi M., Pseudo-differential operator associated with the Dunkl operator, Differ. Integral Equ., 20, pp. 1035-1051, (2007)
[2] Calderon A.P., Vaillancourt R., A class of bounded pseudo-differential operators, Proc. Nat. Acad. Sci. U. S. A., 69, pp. 1185-1187, (1972)
[3] Coifman R.R., Meyer Y., Au-delà des opérateurs pseudo-différentiels, Astérisque, 57, pp. 1-185, (1978)
[4] De Jeu M.F.E., The Dunkl transform, Invent. Math., 113, pp. 147-162, (1993)
[5] Dunkl C.F., Differential-difference operators associated to reflection groups, Trans. Amer. Math. Soc., 311, pp. 167-183, (1989)
[6] Dunkl C.F., Hankel transforms associated to finite reflection groups, Contemp. Math., 138, pp. 123-138, (1992)
[7] Hormander L., On the L2 continuity of pseudo-differential operators, Commun. Pure Appl. Math., 24, pp. 529-535, (1971)
[8] Hwang I.L., The L2-Boundedness of pseudodifferential operators, Trans. Amer. Math. Soc., 302, pp. 55-76, (1987)
[9] Kato T., Boundedness of some pseudo-differential operators, Osaka J. Math., 13, pp. 1-9, (1976)
[10] Kumano-Go H., Nagase M., Lp-theory of pseudo-differential operators, Proc. Jap. Acad., 46, pp. 138-142, (1970)

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