Sobolev inequalities for (0, q) forms on CR manifolds of finite type

Abstract

Let M2n+1 (n ≥ 2) be a compact pseudoconvex CR manifold of finite commutator type whose ∂̄b has closed range in L 2 and whose Levi form has comparable eigenvalues. We prove a Gagliardo-Nirenberg inequality for the ∂̄b complex for (0, q) forms when q ≠ 1 nor n - 1. We also prove an analogous inequality when M satisfies condition Y (q). The main technical ingredient is a new kind of L 1 duality inequality for vector fields that satisfy Hormander's condition. © International Press 2010.