Lp and weighted estimates for barred derivatives

Abstract

We generalize the basic L2 inequality for barred derivatives that holds on bounded pseudoconvex domains. The analogue in Lp-Sobolev norms is established for smooth, bounded pseudoconvex domains of finite type with comparable Levi eigenvalues. A weighted L2 version and Lp estimates with loss are obtained on any smooth bounded weakly q-convex domain, where the weights are fractional powers of the distance to the boundary.