Hardy-Sobolev-Rellich, Hardy-Littlewood-Sobolev and Caffarelli-Kohn-Nirenberg Inequalities on General Lie Groups

作     者：Ruzhansky, Michael Yessirkegenov, Nurgissa 

作者机构：Univ Ghent Dept Math Anal Log & Discrete Math Ghent Belgium Queen Mary Univ London Sch Math Sci London England SDU Univ Kaskelen 040900 Kazakhstan Inst Math & Math Modeling Almaty Alma Ata Kazakhstan 

出 版 物：《JOURNAL OF GEOMETRIC ANALYSIS》 (J Geom Anal)

年 卷 期：2024年第34卷第7期

页      面：1-28页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：Fonds Wetenschappelijk Onderzoek, FWO Ghent University Special Research Fund Ministry of Education and Science of the Republic of Kazakhstan, (AP14871691) Ministry of Education and Science of the Republic of Kazakhstan Engineering and Physical Sciences Research Council, EPSRC, (EP/R003025/2) Engineering and Physical Sciences Research Council, EPSRC Bijzonder Onderzoeksfonds UGent, BOF, (01M01021) Bijzonder Onderzoeksfonds UGent, BOF 

主　　题：Sobolev spaces Sobolev embeddings Hardy inequality Rellich inequality Hardy-Littlewood-Sobolev inequality Caffarelli-Kohn-Nirenberg inequality Lie groups 

摘      要：In this paper, we establish a number of geometrical inequalities such as Hardy, Sobolev, Rellich, Hardy-Littlewood-Sobolev, Caffarelli-Kohn-Nirenberg, Gagliardo-Nirenberg inequalities and their critical versions for an ample class of sub-elliptic differential operators on general connected Lie groups, which include both unimodular and non-unimodular cases in compact and noncompact settings. We also obtain the corresponding uncertainty type principles.