On horizontal Hardy, Rellich, Caffarelli-Kohn-Nirenberg and p-sub-Laplacian inequalities on stratified groups

详细信息    查看全文

• 作者：Michael Ruzhansky^a ; ^{m.ruzhansky@imperial.ac.uk} ; Durvudkhan Suragan^a ; ^b ; ^{d.suragan@imperial.ac.uk}
• 关键词：22E30 ; 43A80
• 刊名：Journal of Differential Equations
• 出版年：2017
• 出版时间：5 February 2017
• 年：2017
• 卷：262
• 期：3
• 页码：1799-1821
• 全文大小：358 K
• 卷排序：262

文摘

In this paper, we present a version of horizontal weighted Hardy–Rellich type and Caffarelli–Kohn–Nirenberg type inequalities on stratified groups and study some of their consequences. Our results reflect on many results previously known in special cases. Moreover, a new simple proof of the Badiale–Tarantello conjecture [2] on the best constant of a Hardy type inequality is provided. We also show a family of Poincaré inequalities as well as inequalities involving the weighted and unweighted p-sub-Laplacians.