An Explicit ∂-integration Formula for Weighted Homogeneous Varieties
نویسنده
چکیده
Let Σ be a weighted homogeneous (singular) subvariety of C . The main objective of this paper is to present an explicit formula for solving the ∂-equation λ = ∂g on the regular part of Σ, where λ is a ∂-closed (0, 1)-form with compact support. This formula will then be used to give Hölder estimates for the solution in case Σ is homogeneous (a cone) with an isolated singularity. Finally, a slight modification of our formula also gives an L-bounded solution operator in case Σ is pure d-dimensional and homogeneous.
منابع مشابه
An Explicit ∂-integration Formula for Weighted Homogeneous Varieties Ii, Forms of Higher Degree
Let Σ be a weighted homogeneous (singular) subvariety of C . The main objective of this paper is to present a class of explicit integral formulae for solving the ∂-equation ω = ∂λ on the regular part of Σ, where ω is a ∂-closed (0, q)-form with compact support and degree q ≥ 1. Particular cases of these formulae yield L-bounded solution operators for 1 ≤ p ≤ ∞ if Σ is a homogeneous and pure dim...
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