Obstructions to uniform estimates for solutions to the d-bar equation
Abstract
Description
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 $\|f\|_\infty$, 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This preprint has been withdrawn by the author because the estimate (2.3) does not follow from the formula preceding it
This preprint has been withdrawn by the author because the estimate (2.3) does not follow from the formula preceding it