On the Solvability of @ in a Class of Hypo-Analytic Manifolds

Abstract

The solvability of @ operator in a class of hypo-analytic manifolds in complex dimension 2 is studied. Suitable weighted L2 spaces are introduced for establishing an a priori inequality. The regularity of the solutions is shown by using a theory of degenerate elliptic operators, developed by Grusin and Visik. The theorem obtained is a degenerate version for the @ problem in strictly pseudo-convex domains.