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Abstract of the third lecture
In the third lecture of this series, you are are to explain how (locally) Sobolev spaces on the Heisenberg group can be seen as Sobolev spaces in the framework of Weyl-H\"ormander calculus. Then after treating some examples, we are going to prove a general restriction theorem for $H^1$ Sobolev spaces in the situation where some vectors fields are transversal. A geometrical interpretation in the case of Heisenberg group will be given.
Abstract of the forth lecture
In this last lecture, you are going to investigate the case when no vector fields are transversal at some point. In the case of the Heisenberg group, we expose a blow up method which will allows to solve the problem under an hypothesis of "non degeneracy".
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