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dc.contributor.author | Ruzhansky, Michael![]() |
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dc.contributor.author | Sabitbek, Bolys![]() |
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dc.contributor.author | Suragan, Durvudkhan![]() |
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dc.date.accessioned | 2021-02-01T08:40:15Z | |
dc.date.available | 2021-02-01T08:40:15Z | |
dc.date.issued | 2020-07-04 | |
dc.identifier.citation | Ruzhansky, M., Sabitbek, B., & Suragan, D. (2020). Geometric Hardy and Hardy–Sobolev inequalities on Heisenberg groups. Bulletin of Mathematical Sciences, 10(03), 2050016. https://doi.org/10.1142/s1664360720500162 | en_US |
dc.identifier.issn | 1664-3615 | |
dc.identifier.issn | 1664-3607 | |
dc.identifier.uri | https://doi.org/10.1142/S1664360720500162 | |
dc.identifier.uri | https://www.worldscientific.com/doi/abs/10.1142/S1664360720500162 | |
dc.identifier.uri | http://nur.nu.edu.kz/handle/123456789/5262 | |
dc.description.abstract | In this paper, we present geometric Hardy inequalities for the sub-Laplacian in half-spaces of stratified groups. As a consequence, we obtain the following geometric Hardy inequality in a half-space of the Heisenberg group with a sharp constant: ∫H+|∇Hu|pdξ≥(p−1p)p∫H+W(ξ)pdist(ξ,∂H+)p|u|pdξ,p>1, which solves a conjecture in the paper [S. Larson, Geometric Hardy inequalities for the sub-elliptic Laplacian on convex domain in the Heisenberg group, Bull. Math. Sci. 6 (2016) 335–352]. Here, W(ξ)=(∑i=1n⟨Xi(ξ),ν⟩2+⟨Yi(ξ),ν⟩2)12 is the angle function. Also, we obtain a version of the Hardy–Sobolev inequality in a half-space of the Heisenberg group: (∫H+|∇Hu|pdξ−(p−1p)p∫H+W(ξ)pdist(ξ,∂H+)p|u|pdξ)1p≥C(∫H+|u|p∗dξ)1p∗, where dist(ξ,∂H+) is the Euclidean distance to the boundary, p∗:=Qp/(Q−p), and 2≤p<Q. For p=2, this gives the Hardy–Sobolev–Maz’ya inequality on the Heisenberg group. | en_US |
dc.language.iso | en | en_US |
dc.publisher | SpringerOpen | en_US |
dc.relation.ispartofseries | Bulletin of Mathematical Sciences;10(03), 2050016 | |
dc.rights | Attribution-NonCommercial-ShareAlike 3.0 United States | * |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-sa/3.0/us/ | * |
dc.subject | Stratified groups | en_US |
dc.subject | Heisenberg group | en_US |
dc.subject | geometric Hardy inequality | en_US |
dc.subject | half-space | en_US |
dc.subject | sharp constant | en_US |
dc.subject | Research Subject Categories::MATHEMATICS | en_US |
dc.title | GEOMETRIC HARDY AND HARDY-SOBOLEV INEQUALITIES ON HEISENBERG GROUPS | en_US |
dc.type | Article | en_US |
workflow.import.source | science |
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