Geometric Hardy and Hardy–Sobolev inequalities on Heisenberg groups

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2018-11-17 DOI:10.1142/s1664360720500162

Michael Ruzhansky, Bolys Sabitbek, D. Suragan

引用次数: 4

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

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。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.