Caffarelli–Kohn–Nirenberg inequalities on Lie groups of polynomial growth

Chokri Yacoub

Mathematische Nachrichten, 2018, vol. 291, issue 1, 204-214

Abstract: In the setting of a Lie group of polynomial volume growth, we derive inequalities of Caffarelli–Kohn–Nirenberg type, where the weights involved are powers of the Carnot–Caratheodory distance associated with a fixed system of vector fields which satisfy the Hörmander condition. The use of weak Lp spaces is crucial in our proofs and we formulate these inequalities within the framework of Lp,q Lorentz spaces (a scale of (quasi)†Banach spaces which extend the more classical Lp Lebesgue spaces) thereby obtaining a refinement of, for instance, Sobolev and Hardy–Sobolev inequalities.

Date: 2018
References: Add references at CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1002/mana.201700063

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:bla:mathna:v:291:y:2018:i:1:p:204-214

Ordering information: This journal article can be ordered from
http://www.blackwell ... bs.asp?ref=0025-584X

Access Statistics for this article

Mathematische Nachrichten is currently edited by Robert Denk

More articles in Mathematische Nachrichten from Wiley Blackwell
Bibliographic data for series maintained by Wiley Content Delivery ().