Improved Lp-Poincaré inequalities on the hyperbolic space. (July 2017)

• Record Type: Journal Article
• Authors: Berchio, Elvise; D'Ambrosio, Lorenzo; Ganguly, Debdip; Grillo, Gabriele
• Is Part Of: Nonlinear analysis. Volume 157(2017)
• Page Start: 146
• Page End: 166
• Publication Date: 2017-07
• Subjects: p-Poincaré inequality -- Hyperbolic space -- Poincaré–Hardy inequality; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2017.03.016
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We investigate the possibility of improving the p -Poincaré inequality ‖ ∇ H N u ‖ p p ≥ Λ p ‖ u ‖ p p on the hyperbolic space, where p > 1 and Λ 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 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.