We find the optimal function norm on the left-hand side of the Formula: see textth order Sobolev type inequality Formula: see text in the Formula: see text-dimensional hyperbolic space Formula: see text, Formula: see text. The optimal function norm in the inequality among all rearrangement-invariant function norms is completely characterized. A variety of concrete examples of optimal function norms is provided. The examples include delicate limiting cases and, especially when Formula: see text, seem to provide new, improved inequalities in these limiting cases.
Zdeněk Mihula (Wed,) studied this question.