A note on the closed range of $${\bar{\partial }}_b$$ on q-convex manifolds

Abstract

We prove that the tangential Cauchy–Riemann operator $${\bar{\partial }}_b$$ has closed range on Levi-pseudoconvex CR manifolds that are embedded in a q-convex complex manifold X. Our result generalizes the known case when X is a Stein manifold (in particular, when $$X={\mathbb C}^n$$ ).