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

被引：0

作者：

Ruzhansky, Michael ^{[1
,2
]}

Yessirkegenov, Nurgissa ^{[3
,4
]}

机构：

[1] Univ Ghent, Dept Math Anal Log & Discrete Math, Ghent, Belgium

[2] Queen Mary Univ London, Sch Math Sci, London, England

[3] SDU Univ, Kaskelen 040900, Kazakhstan

[4] Inst Math & Math Modeling Almaty, Alma Ata, Kazakhstan

来源：

JOURNAL OF GEOMETRIC ANALYSIS | 2024年 / 34卷 / 07期

基金：

英国工程与自然科学研究理事会;

关键词：

Sobolev spaces; Sobolev embeddings; Hardy inequality; Rellich inequality; Hardy-Littlewood-Sobolev inequality; Caffarelli-Kohn-Nirenberg inequality; Lie groups; SPACES;

D O I：

10.1007/s12220-024-01614-9

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

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.

引用

页数：28

共 24 条

[1] The intrinsic hypoelliptic Laplacian and its heat kernel on unimodular Lie groups
Agrachev, Andrei
Boscain, Ugo
Gauthier, Jean-Paul
Rossi, Francesco
[J]. JOURNAL OF FUNCTIONAL ANALYSIS, 2009, 256 (08) : 2621 - 2655
[2] Avetisyan Z., 2024, J. Math. Sci. (N.Y.), V280, P73
[3] The Sobolev embedding constant on Lie groups
Bruno, Tommaso
Peloso, Marco M.
Vallarino, Maria
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2022, 216
[4] Sobolev spaces on Lie groups: Embedding theorems and algebra properties
Bruno, Tommaso
Peloso, Marco M.
Tabacco, Anita
Vallarino, Maria
[J]. JOURNAL OF FUNCTIONAL ANALYSIS, 2019, 276 (10) : 3014 - 3050
[5] Hardy and uncertainty inequalities on stratified Lie groups
Ciatti, Paolo
Cowling, Michael G.
Ricci, Fulvio
[J]. ADVANCES IN MATHEMATICS, 2015, 277 : 365 - 387
[6] Sobolev algebras on Lie groups and Riemannian manifolds
Coulhon, T
Russ, E
Tardivel-Nachef, V
[J]. AMERICAN JOURNAL OF MATHEMATICS, 2001, 123 (02) : 283 - 342
[7] Fischer V, 2016, PROG MATH, V314, P1, DOI 10.1007/978-3-319-29558-9
[8] SOBOLEV SPACES ON GRADED LIE GROUPS
Fischer, Veronique
Ruzhansky, Michael
[J]. ANNALES DE L INSTITUT FOURIER, 2017, 67 (04) : 1671 - 1723
[9] FOLLAND GB, 1975, ARK MAT, V13, P161, DOI 10.1007/BF02386204
[10] GUIVARCH Y, 1973, B SOC MATH FR, V101, P333

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