Sharp estimates for the operator \(\overline{\partial}_M\) on a \(q\)-concave CR-manifold (Q1387673)

Let \(M\) be a regular \(q\)-concave CR-manifold (\(q \geq 2\)) of class \(C^{4}\) and let \(M\) be a relatively compact open subset of \(M\). For any \(r=1, \dots, q-1 \), the author proves the existence of a compact operator \(H_{r}\) and of a linear operator \(R_{r}\) with sharp estimates acting on the space of \((0,r)\)-differential forms such that for such a form \(f\) the following holds for each point \(z\) of \(M\): \( f(z)= \overline{\partial }_{M} R_{r}(f) (z) + R_{r+1} (\overline{\partial }_{M} f) (z) + H_{r}(f) (z) \).