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Trudinger–Moser inequality in the hyperbolic space ℍN

Trudinger–Moser inequality in the hyperbolic space ℍN

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.