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

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 prove that if $\phi$ is a smooth $(0,q+1)$-form on a Stein space $X$ with $\dbar\phi=0$, then there is a smooth $(0,q)$-form $\psi$ on $X_{reg}$ with at most polynomial growth at $X_{sing}$ such that $\dbar\psi=\phi$. The integral formulas also give other new existence results for the $\dbar$-equation and Hartogs theorems, as well as new proofs of various known results.