Advances in Differential Equations

Local Hardy and Rellich inequalities for sums of squares of vector fields

Michael Ruzhansky and Durvudkhan Suragan

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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.


The authors were supported in parts by the EPSRC grant EP/K039407/1 and by the Leverhulme Grant RPG-2014-02, as well as by the MESRK grant 5127/GF4. No new data was collected or generated during the course of the research.

Article information

Adv. Differential Equations, Volume 22, Number 7/8 (2017), 505-540.

Accepted: November 2016
First available in Project Euclid: 4 May 2017

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35A23: Inequalities involving derivatives and differential and integral operators, inequalities for integrals 35H20: Subelliptic equations


Ruzhansky, Michael; Suragan, Durvudkhan. Local Hardy and Rellich inequalities for sums of squares of vector fields. Adv. Differential Equations 22 (2017), no. 7/8, 505--540.

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