Sharp Moser-Trudinger Inequalities on Hyperbolic Spaces with Exact Growth Condition

摘要

Let Phi(n)(x) = e(x) - Sigma(n-2)(j=0) x(j)/j! and alpha(n) = n omega(1-1)(n-1) be the sharp constant in Moser's inequality (where omega(n-1) is the area of the surface of the unit n-ball in R-n), and dV be the volume element on the n-dimensional hyperbolic space (H-n, g) (n >= 2). In this paper, we establish the following sharp Moser-Trudinger type inequalities with the exact growth condition on H-n: