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Improved L$^p$-Poincar\'e inequalities on the hyperbolic space
- Publication Year :
- 2016
-
Abstract
- We investigate the possibility of improving the $p$-Poincar\'e inequality $\|\nabla_{\mathbb{H}^N} u\|_p \ge \Lambda_p \|u\|_p$ on the hyperbolic space, where $p>2$ and $\Lambda_p:=[(N-1)/p]^{p}$ is the best constant for which such inequality holds. We prove several different, and independent, improved inequalities, one of which is a Poincar\'e-Hardy inequality, namely an improvement of the best $p$-Poincar\'e inequality in terms of the Hardy weight $r^{-p}$, $r$ being geodesic distance from a given pole. Certain Hardy-Maz'ya-type inequalities in the Euclidean half-space are also obtained.<br />Comment: File conformal to the printed one. Appeared in Nonlinear Analysis
- Subjects :
- Mathematics - Functional Analysis
Mathematics - Differential Geometry
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1611.08413
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1016/j.na.2017.03.016