Trudinger–Moser inequality in the hyperbolic space ℍN - Mancini Gianni; Sandeep Kunnath; Tintarev Cyril (Advances in Nonlinear Analysis, 2013)
We prove a version of the Trudinger–Moser inequality in the hyperbolic space ℍN, which gives a sharper version of the Trudinger–Moser inequality on the Euclidean unit ball, as well as a hyperbolic space version of the Onofri inequality, and prove the existence of extremal functions to some related problems.