Lp and weighted estimates for barred derivatives

We generalize the basic L-2 inequality for barred derivatives that holds on bounded pseudoconvex domains. The analogue in L-p-Sobolev norms is established for smooth, bounded pseudoconvex domains of finite type with comparable Levi eigenvalues. A weighted L-2 version and L-p 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. (C) 2020 Elsevier Inc. All rights reserved.