On the Ohsawa-Takegoshi L2 extension theorem and the twisted Bochner-Kodaira identity

In this Note, we improve the estimate in Ohsawa's generalization of the Ohsawa-Takegoshi L-2 extension theorem for holomorphic functions by finding a smaller constant, and apply the result to the Suita conjecture. We also present a remark allowing to generalize the Ohsawa-Takegoshi extension theorem to the case of partial derivative-closed smooth (n - 1, q)-forms. Finally, we prove that the twist factor in the twisted Bochner-Kodaira identity can be a non-smooth plurisuperharmonic function. (C) 2011 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.