On the Ohsawa–Takegoshi extension theorem and the twisted Bochner–Kodaira identity

In this Note, we improve the estimate in Ohsawaʼs 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 ∂ ¯ -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.