An explicit d-bar-integration formula for weighted homogeneous varieties II: forms of higher degree

Abstract

Let Y be a weighted homogeneous (singular) subvariety of C^n. The main objective of this paper is to present a class of explicit integral formulae for solving the d-bar-equation $\omega=\dbar\lambda$ on the regular part of Y, where $\omega$ is a d-bar-closed (0,q)-form with compact support and degree q>=1. Particular cases of these formulae yield L^p-bounded solution operators for $1<=p<=\infty$ if Y is a homogeneous and pure dimensional subvariety with an arbitrary singular locus.