We investigate the possibility of improving the optimal Lp-Poincaré inequality on the hyperbolic space, where p>1. We prove several different, and independent, improved inequalities, one of which is a Poincaré–Hardy inequality, namely an improvement of the best Lp-Poincaré inequality in terms of a Hardy weight related to geodesic distance from a given pole. Certain Hardy–Maz’ya-type inequalities in the Euclidean half-space are also obtained.
Improved Lp -Poincaré inequalities on the hyperbolic space
GRILLO, GABRIELE
2017-01-01
Abstract
We investigate the possibility of improving the optimal Lp-Poincaré inequality on the hyperbolic space, where p>1. We prove several different, and independent, improved inequalities, one of which is a Poincaré–Hardy inequality, namely an improvement of the best Lp-Poincaré inequality in terms of a Hardy weight related to geodesic distance from a given pole. Certain Hardy–Maz’ya-type inequalities in the Euclidean half-space are also obtained.File in questo prodotto:
| File | Dimensione | Formato | |
|---|---|---|---|
|
20170304_p_Laplacian.pdf
Accesso riservato
:
Post-Print (DRAFT o Author’s Accepted Manuscript-AAM)
Dimensione
603.61 kB
Formato
Adobe PDF
|
603.61 kB | Adobe PDF | Visualizza/Apri |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
