On estimates for the $\bar{\partial }$ equation in Stein manifolds

Abstract

We generalize to intersection of strictly $c$ -convex domains in Stein manifold, $L^r-L^s$ and Lipschitz estimates for the solutions of the $\bar{\partial }$ equation done by Ma and Vassiliadou for domains in ${\mathbb{C}}^n.$ For this we use a Docquier-Grauert holomorphic retraction plus the raising steps method I introduce earlier. This gives results in the case of domains with low regularity, ${\mathcal{C}}^3,$ for their boundary.

I follow the nice suggestions done by the referee which substantially simplify the proof of theorem 4.1. Also typos are corrected and the presenrtation is slightly modified