ar X iv : 0 80 1 . 07 10 v 2 [ m at h . C V ] 1 1 Fe b 20 08 KOPPELMAN FORMULAS AND THE ∂̄ - EQUATION ON ANALYTIC VARIETIES
نویسندگان
چکیده
Let Z be an analytic subvariety of pure codimension p of a pseudoconvex set X in C n. We introduce a formalism to generate weighted Koppelman formulas on Z that provide solutions to the ¯ ∂-equation. We prove that if φ is a smooth (0, q + 1)-form on Z with ¯ ∂φ = 0, then there is a smooth (0, q)-form ψ on Z reg with at most polynomial growth at Z sing such that ¯ ∂ψ = φ. The integral formulas also admit new proofs of various known existence results for the ¯ ∂-equation, and Hartog theorems for ¯ ∂-closed forms.
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