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arXiv · 1311.0094

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

Xiaolong Han
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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.

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Xiaolong Han. 2013-11-01. Existence of maximizers for Hardy-Littlewood-Sobolev inequalities on the Heisenberg group. https://arxiv.org/abs/1311.0094

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