Sharp constants in several inequalities on the Heisenberg group.(English)Zbl 1252.42023
The authors obtain sharp constants for inequalities on the Heisenberg group whose Euclidean version are the Hardy-Littlewood-Sobolev inequalities. After that, they obtain sharp constants for the Sobolev inequalities for the Laplacian and conformally invariant fractional Laplacians. As a limit case they also obtain sharp constants for the Onofri and log-Sobolev inequalities with different methodology from that used in the Euclidean setting.
Reviewer: Giuseppe Di Fazio (Catania)
MSC:
| 42B35 | Function spaces arising in harmonic analysis |
Cite
References:
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