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Hardy and Rellich inequalities for anisotropic p-sub-Laplacians

被引：5
|
作者：
Ruzhansky, M. [1 ,2 ]
Sabitbek, B. [3 ,4 ]
Suragan, D. [5 ]
机构：
[1] Univ Ghent, Dept Math Anal Log & Discrete Math, Krijgslaan 281,Bldg S8, B-9000 Ghent, Belgium
[2] Queen Mary Univ London, Sch Math Sci, London, England
[3] Inst Math & Math Modeling, 125 Pushkin Str, Alma Ata 050010, Kazakhstan
[4] Al Farabi Kazakh Natl Univ, Alma Ata, Kazakhstan
[5] Nazarbayev Univ, Dept Math, 53 Kabanbay Batyr Ave, Astana 010000, Kazakhstan
来源：
BANACH JOURNAL OF MATHEMATICAL ANALYSIS | 2020年 / 14卷 / 02期
基金：
英国工程与自然科学研究理事会;
关键词：
Stratified group; Anisotropic p-sub-Laplacian; Hardy inequality; Rellich inequality; Picone identity; ULTRAPARABOLIC EQUATIONS;
D O I：
10.1007/s43037-019-00011-7
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper we establish the subelliptic Picone type identities. As consequences, we obtain Hardy and Rellich type inequalities for anisotropic p-sub-Laplacians which are operators of the form L-p f := Sigma(N)(i=1) X-i (vertical bar X-i f vertical bar(pi-2) X-i f), 1 < pi < infinity, where Xi, i=1,...,N, are the generators of the first stratum of a stratified (Lie) group. Moreover, analogues of Hardy type inequalities with multiple singularities and many-particle Hardy type inequalities are obtained on stratified groups.
引用
收藏
页码：380 / 398
页数：19
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