Abstract
Let M be a C-infinity compact CR manifold of CR-codimension l >= 1 and CR- dimension n - l in a complex manifold X of complex dimension n >= 3. In this paper, assuming that M satisfies condition Y(s) for some s with 1 <= s <= n - l - 1, we prove an L-2-existence theorem and global regularity for the solutions of the tangential Cauchy-Riemann equation for (0, s)-forms on M.