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 $\varphi$ is a smooth $(0,q+1)$-form on a Stein space $X$ with $\dbarϕ=0$, then there is a smooth $(0,q)$-form $\psi$ on $X_{reg}$ with at most polynomial growth at $X_{sing}$ such that $\dbarψ=ϕ$. 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.

References in corpus (1)

• Pure Hodge structure on the $L_2$-cohomology of varieties with isolated singularities

Cited by in corpus (6)

• Various approaches to products of residue currents
• Hartogs' extension theorems on Stein spaces
• A Dolbeault-Grothendieck lemma on complex spaces via Koppelman formulas
• Regularizations of residue currents
• On the Briancon-Skoda theorem on a singular variety
• Weighted Koppelman formulas and the $\dbar$-equation on an analytic space