Adams inequality on the hyperbolic space

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• 作者：Debabrata Karmakar ^{debkar@math.tifrbng.res.in" class="auth_mail" title="E-mail the corresponding author} ; Kunnath Sandeep ; ^{sandeep@math.tifrbng.res.in" class="auth_mail" title="E-mail the corresponding author}
• 关键词：46E35 ; 26D10
• 刊名：Journal of Functional Analysis
• 出版年：2016
• 出版时间：1 March 2016
• 年：2016
• 卷：270
• 期：5
• 页码：1792-1817
• 全文大小：450 K

文摘

In this article we establish the following Adams type inequality in the hyperbolic space H^N${\mathbb{H}}^N$: iff β≤β₀(N,k)$\beta \le {\beta }_0(N,k)$ where 6240304aaf230a857102" title="Click to view the MathML source">2k=N$2k=N$, P_k$P_k$ is the critical GJMS operator in H^N${\mathbb{H}}^N$ and β₀(N,k)${\beta }_0(N,k)$ is as defined in (1.3). As an application we prove the asymptotic behaviour of the best constants in Sobolev inequalities when 6240304aaf230a857102" title="Click to view the MathML source">2k=N$2k=N$ and also prove some existence results for the Q_k$Q_k$ curvature type equation in H^N${\mathbb{H}}^N$.