Solutions to $ar{partial}$-equations on strongly pseudo-convex domains with $L^p$-estimates

Abstract

We construct a solution to the $ar{partial}$-equation on a strongly pseudo-convex domain of a complex manifold. This is done for forms of type $(0,s)$, $sgeq 1 $, with values in a holomorphic vector bundle which is Nakano positive and for complex valued forms of type $(r,s)$, $1leq rleq n$, when the complex manifold is a Stein manifold. Using Kerzman's techniques, we find the $L^p$-estimates, $1leq pleq infty$, for the solution.

Keywords

• $L^p$-estimates
• ${partial}$-equation
• strongly pseudo-convex
• smooth boundary
• complex manifolds.