Geometric Hardy inequalities for the sub-elliptic Laplacian on convex domains in the Heisenberg group
2016 (English)In: Bulletin of Mathematical Sciences, ISSN 1664-3607, E-ISSN 1664-3615, Vol. 6, no 3, 335-352 p.Article in journal (Refereed) Published
We prove geometric Lp versions of Hardy’s inequality for the sub-elliptic Laplacian on convex domains Ω in the Heisenberg group Hn, where convex is meant in the Euclidean sense. When p= 2 and Ω is the half-space given by ⟨ ξ, ν⟩ > d this generalizes an inequality previously obtained by Luan and Yang. For such p and Ω the inequality is sharp and takes the form (Formula presented.), where dist(·,∂Ω) denotes the Euclidean distance from ∂Ω.
Place, publisher, year, edition, pages
Springer, 2016. Vol. 6, no 3, 335-352 p.
IdentifiersURN: urn:nbn:se:kth:diva-195306DOI: 10.1007/s13373-016-0083-4ISI: 000385157400001ScopusID: 2-s2.0-84991388174OAI: oai:DiVA.org:kth-195306DiVA: diva2:1045770
FunderSwedish Research Council, 2012-3864
QC 201611102016-11-102016-11-022016-11-11Bibliographically approved