Hardy and Rellich inequalities, identities, and sharp remainders on homogeneous groups

Michael Ruzhansky, Durvudkhan Suragan

Research output: Contribution to journalArticle

18 Citations (Scopus)


We give sharp remainder terms of Lp and weighted Hardy and Rellich inequalities on one of most general subclasses of nilpotent Lie groups, namely the class of homogeneous groups. As consequences, we obtain analogues of the generalised classical Hardy and Rellich inequalities and the uncertainty principle on homogeneous groups. We also prove higher order inequalities of Hardy–Rellich type, all with sharp constants. A number of identities are derived including weighted and higher order types.

Original languageEnglish
Pages (from-to)799-822
Number of pages24
JournalAdvances in Mathematics
Publication statusPublished - Sep 7 2017
Externally publishedYes



  • Homogeneous Lie group
  • L-Hardy inequality
  • Rellich inequality
  • Uncertainty principle
  • Weighted Hardy inequality

ASJC Scopus subject areas

  • Mathematics(all)

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