Heisenberg群上的几何Hardy和Hardy - sobolev不等式

IF 1.1 2区数学 Q1 MATHEMATICS

Bulletin of Mathematical Sciences Pub Date : 2018-11-17 DOI:10.1142/s1664360720500162

Michael Ruzhansky, Bolys Sabitbek, D. Suragan

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引用次数: 4

摘要

本文给出了层群半空间中次拉普拉斯的几何Hardy不等式。因此，我们在Heisenberg群的半空间中得到了具有尖锐常数的几何Hardy不等式:[公式:见文]，它解决了论文[S]中的一个猜想。在Heisenberg群的凸域上的次椭圆拉普拉斯几何Hardy不等式。数学。科学6(2016)335-352。其中，[公式:见正文]为角度函数。同时，我们得到了海森堡群半空间中的Hardy-Sobolev不等式的一个版本:[公式:见文]，其中[公式:见文]是到边界的欧几里得距离，[公式:见文]，和[公式:见文]。对于[公式:见原文]，这给出了海森堡群上的Hardy-Sobolev-Maz 'ya不等式。

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Geometric Hardy and Hardy–Sobolev inequalities on Heisenberg groups

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: [Formula: see text] 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, [Formula: see text] is the angle function. Also, we obtain a version of the Hardy–Sobolev inequality in a half-space of the Heisenberg group: [Formula: see text] where [Formula: see text] is the Euclidean distance to the boundary, [Formula: see text], and [Formula: see text]. For [Formula: see text], this gives the Hardy–Sobolev–Maz’ya inequality on the Heisenberg group.

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来源期刊

Bulletin of Mathematical Sciences MATHEMATICS-

CiteScore

2.10

自引率

0.00%

发文量

审稿时长

13 weeks

期刊介绍： The Bulletin of Mathematical Sciences, a peer-reviewed, open access journal, will publish original research work of highest quality and of broad interest in all branches of mathematical sciences. The Bulletin will publish well-written expository articles (40-50 pages) of exceptional value giving the latest state of the art on a specific topic, and short articles (up to 15 pages) containing significant results of wider interest. Most of the expository articles will be invited. The Bulletin of Mathematical Sciences is launched by King Abdulaziz University, Jeddah, Saudi Arabia.