New Progress on Weighted Trudinger–Moser and Gagliardo–Nirenberg, and Critical Hardy Inequalities on Stratified Groups

  • Michael RuzhanskyEmail author
  • Nurgissa Yessirkegenov
Part of the Applied and Numerical Harmonic Analysis book series (ANHA)


In this paper, we present a summary of our recent research on local and global weighted (singular) Trudinger–Moser inequalities with remainder terms, critical Hardy-type and weighted Gagliardo–Nirenberg inequalities on general stratified groups. These include the cases of \(\mathbb R^n\) and Heisenberg groups. Moreover, the described critical Hardy-type inequalities give the critical case of the Hardy-type inequalities from [4].


Trudinger–Moser inequality Critical Hardy inequality Stratified Lie groups 

2010 Mathematics Subject Classification:

46E35 22E30 43A80 


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Authors and Affiliations

  1. 1.Department of Mathematics: Analysis, Logic and Discrete MathematicsGhent University, Belgium and School of Mathematical Sciences, Queen Mary University of LondonLondonUK
  2. 2.Department of MathematicsImperial College LondonLondonUK
  3. 3.Institute of Mathematics and Mathematical ModellingAlmatyKazakhstan

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