Electronic Journal of Differential Equations,
Vol. 2004(2004), No. 73, pp. 1-9.

Title: Solutions to $\bar{\partial}$-equations on strongly 
       pseudo-convex domains with $L^p$-estimates

Authors: Osama Abdelkader (Minia Univ., El-Minia, Egypt)
         Shaban Khidr   (Cairo Univ., Beni- Suef, Egypt)

Abstract:
 We construct a solution to the $\bar{\partial}$-equation on
 a strongly pseudo-convex domain of a complex manifold.
 This is done for forms of type $(0,s)$, $s\geq 1 $,
 with values in a holomorphic vector bundle which is  Nakano
 positive and for complex valued forms of type $(r,s)$,
 $1\leq r\leq n$, when the complex manifold is a Stein manifold.
 Using Kerzman's techniques, we find the $L^p$-estimates,
 $1\leq p\leq \infty$, for the solution.
  
Submitted March 01, 2004. Published May 20, 2004.
Math Subject Classifications: 32F27, 32C35, 35N15.
Key Words: $L^p$-estimates; $\bar{\partial}$-equation; strongly pseudo-convex;
           smooth boundary; complex manifolds.