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Complex Analysis and Operator Theory

, Volume 12, Issue 6, pp 1469–1480 | Cite as

Horizontal Weighted Hardy–Rellich Type Inequalities on Stratified Lie Groups

  • Bolys SabitbekEmail author
  • Durvudkhan Suragan
Article
  • 94 Downloads

Abstract

This paper is devoted to present a version of horizontal weighted Hardy–Rellich type inequality on stratified Lie groups and study some of its consequences. In particular, Sobolev type spaces are defined on stratified Lie groups and proved embedding theorems for these functional spaces.

Keywords

Hardy–Rellich inequality Caffarelli–Kohn–Nirenberg inequality Horizontal estimate Stratified group Sobolev type spaces Embedding theorem 

Mathematics Subject Classification

22E30 43A80 

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Copyright information

© Springer International Publishing 2017

Authors and Affiliations

  1. 1.Institute of Mathematics and Mathematical ModellingAlmatyKazakhstan
  2. 2.Al-Farabi Kazakh National UniversityAlmatyKazakhstan

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