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We derive the sharp constants for the inequalities on the Heisenberg group H^n whose analogues on Euclidean space R^n are the well known Hardy-Littlewood-Sobolev inequalities.
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W. Beckner, Sobolev inequalities, the Poisson semigroup, and analysis on the sphere 𝕊 n \mathbb{S}^{n}
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2007
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2008
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H. Bahouri, I. Gallagher, The heat kernel and frequency localized functions on the Heisenberg group
2009
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R. L. Frank, E. H. Lieb, Inversion positivity and the sharp Hardy-Littlewood-Sobolev inequality
2010
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R. L. Frank, E. H. Lieb, A new, rearrangement-free proof of the sharp Hardy-Littlewood-Sobolev inequality
2011
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