Weighted Koppelman formulas and the $\dbar$-equation on an analytic space

TL;DR

This paper develops intrinsic weighted Koppelman formulas on analytic spaces to solve the $ar{ ext{d}}$-equation, leading to new existence results and alternative proofs for classical theorems.

Contribution

It introduces a formalism for intrinsic weighted Koppelman formulas on analytic spaces, advancing the understanding of the $ar{ ext{d}}$-equation solutions.

Findings

New existence results for the $ar{ ext{d}}$-equation

Alternative proofs of classical results

Development of intrinsic weighted Koppelman formulas

Abstract

Let $X$ be an analytic space of pure dimension. We introduce a formalism to generate intrinsic weighted Koppelman formulas on $X$ that provide solutions to the $\dbar$-equation. We obtain new existence results for the $\dbar$-equation, as well as new proofs of various known results.