Obstructions to uniform estimates for solutions to the d-bar equation

Abstract

We show that if, for every bounded d-bar-closed (0,1)-form f, a pseudoconvex domain Ωadmits a solution to $\bar{\partial }u=f$ that is continuous up to the boundary and has uniform estimates in terms of $\Vert f{\Vert }_{\infty }$, then each p\in bdy(Ω) must necessarily admit a peak function in the class $A(Ω):=\mathcal{O}(Ω)\cap\mathcal{C}(\overline\OM)$. We use this fact to examine some geometrical obstructions to uniform estimates for the d-bar equation.

This preprint has been withdrawn by the author because the estimate (2.3) does not follow from the formula preceding it