| Recently Bourgain-Brezis and Lanzani-Stein proved a Gagliardo-Nirenberg-Sobolev inequality for differential forms on Rn : If u is a smooth compactly supported q form on Rn and q &ne 1 nor n - 1, then u Lnn-1 Rn&lsim du L1Rn +d* uL1 Rn . In this thesis, we prove an analog of this result for the &partb complex on a large class of CR manifolds of finite commutator type. The main innovation here is a new kind of L1 div-curl inequality for vector fields that satisfy Hormander's condition, generalizing the recent work of Chanillo-van Schaftingen. |
