Horizontal Weighted Hardy–Rellich Type Inequalities on Stratified Lie Groups

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.

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Correspondence to Bolys Sabitbek.

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The authors were supported by the MESRK Grant 5127/GF4.

Communicated by Michael Ruzhansky.

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Sabitbek, B., Suragan, D. Horizontal Weighted Hardy–Rellich Type Inequalities on Stratified Lie Groups. Complex Anal. Oper. Theory 12, 1469–1480 (2018). https://doi.org/10.1007/s11785-017-0650-z

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Keywords

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

Mathematics Subject Classification

  • 22E30
  • 43A80