[HTML][HTML] On horizontal Hardy, Rellich, Caffarelli–Kohn–Nirenberg and p-sub-Laplacian inequalities on stratified groups
M Ruzhansky, D Suragan - Journal of Differential Equations, 2017 - Elsevier
Journal of Differential Equations, 2017•Elsevier
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.
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.
Abstract
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.
Elsevier
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