Existence of maximizers for Hardy-Littlewood-Sobolev inequalities on the Heisenberg group

Abstract

In this paper, we investigate the sharp Hardy-Littlewood-Sobolev inequalities on the Heisenberg group. On one hand, we apply the concentration compactness principle to prove the existence of the maximizers. While the approach here gives a different proof under the special cases discussed in a recent work of Frank and Lieb, we generalize the result to all admissible cases. On the other hand, we provide the upper bounds of sharp constants for these inequalities.

To be published in Indiana University Mathematics Journal

References in corpus (1)

• Sharp constants in several inequalities on the Heisenberg group