Solutions to ∂¯-equations on strongly pseudo-convex domains with Lᵖ-estimates

Abstract

We construct a solution to the ∂¯-equation on a strongly pseudo-convex domain of a complex manifold. This is done for forms of type (0, s), for complex valued forms of type (r, s), 1 ≤ r ≤ n, when the complex manifold is a Stein manifold. Using Kerzman's techniques, we find the Lp-estimates, 1 ≤ p ≤ ∞, for the solution.