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Best constants for Moser-Trudinger inequalities on the Heisenberg group. (English) Zbl 1019.43009
The authors prove a Moser-Trudinger inequality with sharp constant on the Heisenberg group. A representation formula for a smooth function in terms of its subgradient is also obtained.

MSC:
43A99 Abstract harmonic analysis
35J15 Second-order elliptic equations
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
22E25 Nilpotent and solvable Lie groups
58E35 Variational inequalities (global problems) in infinite-dimensional spaces
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