Existence of maximizers for Hardy-Littlewood-Sobolev inequalities on the Heisenberg group
Xiaosen Han
39B6249J4535R03Hardy-Littlewood-Sobolev inequalities on the Heisenberg groupconcentration compactness principleexistence of maximizersupper bounds of sharp constants
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.
Indiana University Mathematics Journal
2013
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10.1512/iumj.2013.62.4976
10.1512/iumj.2013.62.4976
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Indiana Univ. Math. J. 62 (2013) 737 - 751
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