Local hardy and rellich inequalities for sums of squares of vector fields

Michael Ruzhansky, Durvudkhan Suragan

Research output: Contribution to journalArticle

14 Citations (Scopus)

Abstract

We prove local refined versions of Hardy's and Rellich's inequalities as well as of uncertainty principles for sums of squares of vector fields on bounded sets of smooth manifolds under certain assumptions on the vector fields. We also give some explicit examples, in particular, for sums of squares of vector fields on Euclidean spaces and for sub-Laplacians on stratified Lie groups.

Original languageEnglish
Pages (from-to)505-540
Number of pages36
JournalAdvances in Differential Equations
Volume22
Issue number7-8
Publication statusPublished - Jul 1 2017
Externally publishedYes

Fingerprint

Sum of squares
Vector Field
Sub-Laplacian
Lie groups
Uncertainty Principle
Smooth Manifold
Bounded Set
Euclidean space

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Cite this

Local hardy and rellich inequalities for sums of squares of vector fields. / Ruzhansky, Michael; Suragan, Durvudkhan.

In: Advances in Differential Equations, Vol. 22, No. 7-8, 01.07.2017, p. 505-540.

Research output: Contribution to journalArticle

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