Lipschitz and Triebel-Lizorkin spaces associated with the Dunkl operators on Rd

被引：0
|
作者：
Kallel, Samir [1 ,2 ]
机构：
[1] Univ Tunis El Manar, Fac Sci Tunis, Lab Anal Math & Applicat LR11ES11, El Manar 1, Tunis 2092, Tunisia
[2] Monastir Univ, Higher Inst Comp Sci & Math Monastir, Dept Math, Monastir 5000, Tunisia
来源：
POSITIVITY | 2019年 / 23卷 / 05期
关键词：
Dunkl operators; Dunkl-Poisson transforms; Dunkl-Lipschitz spaces; Dunkl-Triebel-Lizorkin spaces; Dunkl-Flett potentials; BESOV-SPACES; TEMPERATURES; POTENTIALS;
D O I：
10.1007/s11117-019-00650-y
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper we define Lipschitz and Triebel-Lizorkin spaces associated with the differential-difference Dunkl operators on Rd. We study inclusion relations among them. Next, some interpolation results and continuity results of some important operators (the Dunkl-Poisson semigroup and Dunkl-Flett potentials) on them are established. Also, we prove certain inclusion relations between Dunkl-Sobolev classes L alpha,kp(R-d) of positive fractional order alpha, Dunkl-Lipschitz spaces perpendicular to alpha,p,qk(R-d) and Dunkl-Triebel-Lizorkin spaces F alpha,p,qk(R-d).
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页码：1021 / 1049
页数：29
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