Lp estimates for the (partial derivative)over-bar-equation on a class of infinite type domains

We prove L-p estimates, 1 <= p <= 8, for solutions to the Cauchy- Riemann equations (partial derivative) over baru = phi on a class of infinite type domains in C-2. The domains under consideration are a class of convex ellipsoids, and we show that if phi is a (partial derivative) over bar -closed ( 0, 1)-form with coefficients in Lp and u is the Henkin kernel solution to (partial derivative) over baru = phi, then parallel to u parallel to(p) <= C parallel to phi parallel to(p) where the constant C is independent of phi In particular, we prove L-1 estimates and obtain L-p estimates by interpolation.