### 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 language | English |
---|---|

Pages (from-to) | 505-540 |

Number of pages | 36 |

Journal | Advances in Differential Equations |

Volume | 22 |

Issue number | 7-8 |

Publication status | Published - Jul 1 2017 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Analysis
- Applied Mathematics

### Cite this

*Advances in Differential Equations*,

*22*(7-8), 505-540.

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

Research output: Contribution to journal › Article

*Advances in Differential Equations*, vol. 22, no. 7-8, pp. 505-540.

}

TY - JOUR

T1 - Local hardy and rellich inequalities for sums of squares of vector fields

AU - Ruzhansky, Michael

AU - Suragan, Durvudkhan

PY - 2017/7/1

Y1 - 2017/7/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85019088337&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85019088337&partnerID=8YFLogxK

M3 - Article

VL - 22

SP - 505

EP - 540

JO - Advances in Differential Equations

JF - Advances in Differential Equations

SN - 1079-9389

IS - 7-8

ER -