Semiglobal results for \(\overline{\partial}_b\) on weakly convex hypersurfaces in \(\mathbb{C}^n\) (Q1593022)

Let \(M\) be the boundary of a smoothly bounded weakly convex domain in \(\mathbb{C}^n\), \(n\geq 4\). The author derives a homotopy formula for \((0,q)\)-forms on certain smoothly bounded subsets \(w\) of \(M\), when \(1\leq q\leq n-2\). The homotopy operators satisfy estimates up to the boundary of \(w\). As a corollary, solvability of \(\overline \partial_b\) in \(C^\infty (\overline w)\) is obtained.