LP-Fourier multipliers for the Dunkl operator on the real line

被引:54
作者
Soltani, F [1 ]
机构
[1] Fac Sci Tunis, Dept Math, Tunis 1060, Tunisia
关键词
Dunkl operator; Dunkl transform; L-P-multipliers;
D O I
10.1016/j.jfa.2003.11.009
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We consider Fourier multipliers for L-P associated with the Dunkl operator on R and establish a version of Hormander's multiplier theorem. In applying this version, we come up with some results regarding the oscillating multipliers, partial sum operators and generalized Bessel potentials. (C) 2004 Elsevier Inc. All rights reserved.
引用
收藏
页码:16 / 35
页数:20
相关论文
共 20 条
[1]   LP FOURIER MULTIPLIERS ON RIEMANNIAN SYMMETRICAL SPACES OF THE NONCOMPACT TYPE [J].
ANKER, JP .
ANNALS OF MATHEMATICS, 1990, 132 (03) :597-628
[2]   The Calogero-Sutherland model and generalized classical polynomials [J].
Baker, TH ;
Forrester, PJ .
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1997, 188 (01) :175-216
[3]  
Bergh J., 1976, GRUNDLEHREN MATH WIS, V223
[4]   Fourier multipliers for Lp on Chebli-Trimeche hypergroups [J].
Bloom, WR ;
Xu, ZF .
PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, 2000, 80 :643-664
[5]   A UNIFICATION OF KNIZHNIK-ZAMOLODCHIKOV AND DUNKL OPERATORS VIA AFFINE HECKE ALGEBRAS [J].
CHEREDNIK, I .
INVENTIONES MATHEMATICAE, 1991, 106 (02) :411-431
[6]  
Coifman RR., 1971, Lect. Notes Math., DOI 10.1007/BFb0058946
[7]   THE DUNKL TRANSFORM [J].
DEJEU, MFE .
INVENTIONES MATHEMATICAE, 1993, 113 (01) :147-162
[8]  
DEMICHELE L, 1980, J FUNCT ANAL, V39, P1, DOI 10.1016/0022-1236(80)90015-4
[10]   INTEGRAL-KERNELS WITH REFLECTION GROUP INVARIANCE [J].
DUNKL, CF .
CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, 1991, 43 (06) :1213-1227