Abstract
In this note, we prove an L-2-existence theorem for the partial derivative-Neumann operator and the regularity for the partial derivative-equation on an annulus type domain D = D-1 \ (D-2) over bar, where D-1 and D-2 are strictly pseudoconvex domains with smooth boundaries in a Stein manifold X of complex dimension n >= 3, such that (D-2) over bar subset of D-1 sic X. Moreover, we obtain Holder and L-P estimates for the partial derivative-equation on strictly pseudoconcave domains with smooth C-3-boundaries in X. (C) 2013 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.