On the Solvability of (DELTA) in a Class of Hypo-Analytic Manifolds

The solvability of (DELTA) operator in a class of hypo-analytic manifolds in complex dimension 2 is studied. Suitable weighted L^2 spaces are introduced for establishing an a priori inequality. The regularity of the solutions is shown by using a theory of degenerate elliptic oyerators, developed by Grusin and Visik. The theorem obtained is a degenerate version for the (DELTA) problem in strictly pseudo-convex domains.