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


Department of Mathematics,Sharif University of Technology


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.