As an application of a sharp extension theorem for holomorphic functions in Guan and Zhou, a stability theorem for the boundary asymptotics of the Bergman kernel is proved. An alternate proof of the extension theorem is given, too. It is a simplified proof in the sense that it is free from ordinary differential equations.
"Application and simplified proof of a sharp extension theorem." Nagoya Math. J. 220 81 - 89, December 2015. https://doi.org/10.1215/00277630-3335780