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Abstract. A general extension theorem for L 2 holomorphic bundle-valued top forms is formulated. Although its proof is based on a principle similar to Ohsawa-Takegoshi's extension theorem, it explains previous L 2 extendability results systematically and bridges extension theory and division theory.

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Let D be a bounded pseudoconvex domain in Cn, and let KD (z, w) be the Bergman kernel function of D. The boundary behavior of KD (z, w), or that of KD (z, z), has attracted a lot of attention because it is closely related to the pseudoconformal geometry of D and ∂D.