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- W2799692574 abstract "We establish several Poincare--Sobolev type inequalities for the Lapalce--Beltrami operator $Delta_g$ in the hyperbolic space $mathbb H^n$ with $ngeq 5$. These inequalities could be seen as the improved second order Poincare inequality with remainder terms involving with the sharp Rellich inequality or sharp Sobolev inequality in $mathbb H^n$. The novelty of these inequalities is that it combines both the sharp Poincare inequality and the sharp Rellich inequality or the sharp Sobolev inequality for $Delta_g$ in $mathbb H^n$. As a consequence, we obtain the Poincare--Sobolev inequality for the second order GJMS operator $P_2$ in $mathbb H^n$. In dimension $4$, we obtain an improvement of the sharp Adams inequality and an Adams inequality with exact growth for radial functions in $mathbb H^4$." @default.
- W2799692574 created "2018-05-17" @default.
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- W2799692574 date "2018-05-05" @default.
- W2799692574 modified "2023-09-27" @default.
- W2799692574 title "Second order Sobolev type inequalities in the hyperbolic spaces" @default.
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