Article ID Journal Published Year Pages File Type
5024644 Nonlinear Analysis: Theory, Methods & Applications 2017 21 Pages PDF
Abstract
We investigate the possibility of improving the p-Poincaré inequality ‖∇HNu‖pp≥Λp‖u‖pp on the hyperbolic space, where p>1 and Λp:=[(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 Poincaré-Hardy inequality, namely an improvement of the best p-Poincaré 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.
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Physical Sciences and Engineering Engineering Engineering (General)
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