Archivio Istituzionale della RicercaWe investigate the possibility of improving the p-Poincare inequality parallel to on the hyperbolic space, where p > 1. We prove several different, and independent, improved inequalities, one of which is a Poincare-Hardy inequality, namely an improvement of the best p-Poincare inequality in terms of the Hardy weight 1/r^p, r being geodesic distance from a given pole. Certain Hardy-Mazya type inequalities in the Euclidean half-space are also obtained.
Improved Lp-Poincaré inequalities on the hyperbolic space / Berchio, Elvise; D'Ambrosio, Lorenzo; Ganguly, Debdip; Grillo, Gabriele. - In: NONLINEAR ANALYSIS. - ISSN 0362-546X. - 157:(2017), pp. 146-166. [10.1016/j.na.2017.03.016]
Improved Lp-Poincaré inequalities on the hyperbolic space
BERCHIO, ELVISE;
2017
Abstract
We investigate the possibility of improving the p-Poincare inequality parallel to on the hyperbolic space, where p > 1. We prove several different, and independent, improved inequalities, one of which is a Poincare-Hardy inequality, namely an improvement of the best p-Poincare inequality in terms of the Hardy weight 1/r^p, r being geodesic distance from a given pole. Certain Hardy-Mazya type inequalities in the Euclidean half-space are also obtained.
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https://hdl.handle.net/11583/2675840
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