Sharp Moser–Trudinger Inequalities on Hyperbolic Spaces with Exact Growth Condition

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• 作者：Guozhen Lu ; Hanli Tang
• 关键词：Hyperbolic spaces ; Sharp Moser–Trudinger inequalities ; Best constants ; Exact growth condition
• 刊名：Journal of Geometric Analysis
• 出版年：2016
• 出版时间：April 2016
• 年：2016
• 卷：26
• 期：2
• 页码：837-857
• 全文大小：487 KB
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• 作者单位：Guozhen Lu (1) (2)
  Hanli Tang (1)
  
  1. School of Mathematical Sciences, Beijing Normal University, Beijing, 100875, China
  2. Department of Mathematics, Wayne State University, Detroit, MI, 48202, USA
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Differential Geometry
  Convex and Discrete Geometry
  Fourier Analysis
  Abstract Harmonic Analysis
  Dynamical Systems and Ergodic Theory
  Global Analysis and Analysis on Manifolds
  
• 出版者：Springer New York
• ISSN：1559-002X

文摘

Let \(\Phi _{n}(x)=e^x-\sum _{j=0}^{n-2}\frac{x^j}{j!}\) and \(\alpha _{n} =n\omega _{n-1}^{\frac{1}{n-1}}\) be the sharp constant in Moser’s inequality (where \(\omega _{n-1}\) is the area of the surface of the unit \(n\)-ball in \(\mathbb {R}^n\)), and \(dV\) be the volume element on the \(n\)-dimensional hyperbolic space \((\mathbb {H}^n, g)\) (\(n\ge {2}\)). In this paper, we establish the following sharp Moser–Trudinger type inequalities with the exact growth condition on \(\mathbb {H}^n\):