Optimal Sobolev estimates for �? on convex domains of finite type

Abstract

We prove that solutions for ¯∂ get 1/M-derivatives more than the data in L p -Sobolev spaces on a bounded convex domain of finite type M by means of the integral kernel method. Also we prove that the Bergman projection is invariant under the L p -Sobolev spaces of fractional orders by different methods from McNeal-Stein's. By using these results, we can get L p -Sobolev estimates of order 1/M for the canonical solution for ¯∂.