Adams inequality with exact growth in the hyperbolic space ℍ4 and Lions lemma

Abstract

In this paper, we prove Adams inequality with exact growth condition in the four-dimensional hyperbolic space [Formula: see text] [Formula: see text] [Formula: see text]. We will also establish an Adachi–Tanaka-type inequality in this setting. Another aspect of this paper is the Lions lemma in the hyperbolic space. We prove Lions lemma for the Moser functional and for a few cases of the Adams functional on the whole hyperbolic space.