Rellich, Gagliardo-Nirenberg, Trudinger and Caffarelli-Kohn-Nirenberg inequalities for Dunkl operators and applications

被引：3
|
作者：
Velicu, Andrei [1 ,2 ]
Yessirkegenov, Nurgissa [3 ,4 ,5 ]
机构：
[1] Imperial Coll London, Dept Math, Huxley Bldg,180 Queens Gate, London SW7 2AZ, England
[2] Univ Paul Sabatier, Inst Math Toulouse, 118 Route Narbonne, F-31062 Toulouse, France
[3] Univ Ghent, Dept Math Anal Log & Discrete Math, 281 Krijgslaan,Bldg S8, Ghent, Belgium
[4] Suleyman Demirel Univ, Kaskelen, Kazakhstan
[5] Inst Math & Math Modeling, 125 Pushkin Str, Alma Ata 050010, Kazakhstan
来源：
ISRAEL JOURNAL OF MATHEMATICS | 2022年 / 247卷 / 02期
基金：
英国工程与自然科学研究理事会;
关键词：
RIESZ-POTENTIALS; MAXIMAL-FUNCTION; L-P; TRANSFORM; PROOF;
D O I：
10.1007/s11856-021-2261-7
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper we introduce several extended versions of the classical Caffarelli-Kohn-Nirenberg inequalities. Moreover, we obtain weighted higher order Rellich, weighted Gagliardo-Nirenberg, Caffarelli-Kohn-Nirenberg, Trudinger inequalities and the uncertainty principle for Dunkl operators. Furthermore, we give an application of the Gagliardo-Nirenberg inequality to the Cauchy problem for the nonlinear damped wave equations for the Dunkl Laplacian.
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页码：741 / 782
页数：42
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