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

Authors: Xiaolong Han

Issue: Volume 62 (2013), Issue 3, 737-751


In this paper, we investigate the sharp Hardy-Littlewood-So\-bo\-lev inequalities on the Heisenberg group. On the 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 [\textit{Sharp constants in several inequalities on the Heisenberg group}, preprint], we generalize the result to all admissible cases. On the other hand, we provide the upper bounds of sharp constants for these inequalities.