Geodesic
Bergman kernels for almost spherical domians with $H^{\sigma}$-smoth boundaries
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 29, Tome 282 (2001), pp. 66-73 
E. G. Zel'dina. Bergman kernels for almost spherical domians with $H^{\sigma}$-smoth boundaries. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 29, Tome 282 (2001), pp. 66-73. http://geodesic.mathdoc.fr/item/ZNSL_2001_282_a5/
@article{ZNSL_2001_282_a5,
     author = {E. G. Zel'dina},
     title = {Bergman kernels for almost spherical domians with $H^{\sigma}$-smoth boundaries},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {66--73},
     year = {2001},
     volume = {282},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2001_282_a5/}
}
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This paper is devoted to the behavior of the Bergman kernels for almost spherical striclty pseudoconvex domians in $\mathbb C^n$. We find first several terms of the asymptotics for the Bergman kernel of striclty pseudoconvex domian with $H^{\sigma}$-smooth boundary, $4<\sigma<6$. New terms in comparison with the case of $C^6$-smoth boundary appear but the growth rate of the remainder remains the same.